(*    F2p - NLO - LaplaceTransform     *)

(* Input PDF at Q0^2 = 2 GeV^2 from GJR08  Ref: Eur Phys J C 53,355-366 (2008) *)

xuv=0.3753 (x^0.3126)(((1-x))^3.6536)(1+3.2716 (x^0.5036)+21.2864 x);
xdv=0.6124 (x^0.4226)(((1-x))^5.1529)(1-3.7475 (x^0.9553)+14.138 x);
xs=0.3506 (x^(-0.1775))(((1-x))^8.9898)(1+0.4549 (x^0.8764)+12.4246 x);
(*xs=0.175368 (x^(-0.1775))(((1-x))^8.9898)(1+0.4549 (x^0.8764)+12.4246 x);*)
xdbarPubar= 0.8 xs;
xdbarMubar=15.8096 (x^1.443)(((1-x))^(10.4343+8.9898))(1-7.5151 (x^0.4972)+20.4901 x);
xg=7.1383 (x^0.1348)(((1-x))^10.0188)(1+1.3264 (x^2)-0.9499 x);
xsbar= 0.2 xs;

x=Exp[-v];

Un=LaplaceTransform[xuv,v,s]
Dn=LaplaceTransform[xdv,v,s]
gn=LaplaceTransform[xg,v,s]
dbarPubarn=LaplaceTransform[xdbarPubar,v,s]
dbarMubarn=LaplaceTransform[xdbarMubar,v,s]
sbarn=LaplaceTransform[xsbar,v,s]

sgi=Un+Dn+2 dbarPubarn+2 sbarn;
gli=gn;
m3i=Un-Dn;
vai=Un+Dn;
m8i=vai;
p3i=m3i-2 dbarMubarn;
p8i=sgi-3  sbarn;

Λ=lan^2;
Q0=2;

β0=11-(2/3)f;
β1=102-(38/3)f;
"Q=Input["Q"]"; 
αQ=4Pi((1/(β0*(y-Log[Λ])))-((β1)/(((β0))^3))((Log[y-Log[Λ]])/(((y-Log[Λ]))^2)));
αQ0=4Pi((1/(β0*(y0-Log[Λ])))-((β1)/(((β0))^3))((Log[y0-Log[Λ]])/(((y0-Log[Λ]))^2)));

AlfasQ=αQ;
AlfasQ0=αQ0;
(*αQ=4Pi((1/(β0*(y-Log[Λ]))));
αQ0=4Pi((1/(β0*(y0-Log[Λ]))));*)
taQ=Integrate[1/(4Pi)AlfasQ,y]/.y->Log[Q];
taQ0=Integrate[1/(4Pi)AlfasQ0,y0]/.y0->Log[Q0];
ta=taQ-taQ0;
cf=(4/3);
ca=3;
 tf=f;
tr=f/2;
(*lan=0.468*)

ta2n=(1/(β0^6))(-((2 β1^2)/(27 (Log[Q]-Log[Λ])^3))+(β0^2 β1)/(2 (Log[Q]-Log[Λ])^2)-β0^4/(Log[Q]-Log[Λ])+(β1 (-2 β1+9 β0^2 (Log[Q]-Log[Λ])) Log[Log[Q]-Log[Λ]])/(9 (Log[Q]-Log[Λ])^3)-(β1^2 Log[Log[Q]-Log[Λ]]^2)/(3 (Log[Q]-Log[Λ])^3))-(1/(β0^6))(-((2 β1^2)/(27 (Log[Q0]-Log[Λ])^3))+(β0^2 β1)/(2 (Log[Q0]-Log[Λ])^2)-β0^4/(Log[Q0]-Log[Λ])+(β1 (-2 β1+9 β0^2 (Log[Q0]-Log[Λ])) Log[Log[Q0]-Log[Λ]])/(9 (Log[Q0]-Log[Λ])^3)-(β1^2 Log[Log[Q0]-Log[Λ]]^2)/(3 (Log[Q0]-Log[Λ])^3));

"Lo Input Spliting Function";



pqq0=4-8/3(1/(s+1)+1/(s+2)+2(EulerGamma+PolyGamma[0,s+1]));
(*δpqq0=cf ((3/2)+HarmonicNumber[s]-HarmonicNumber[2+s])*)
pqg0=((1/(1+s))-(2/(2+s))+(2/(3+s))) tr;
pgq0=cf ((2/s)-(2/(1+s))+(1/(2+s)));
pgg0=12((1/s)-((2 )/(1+s))+((2 )/(2+s))-((1 )/(3+s))-(EulerGamma+PolyGamma[0,s+1]))+((33-2 f)/3);

pnsp1=cf tf (-(2/(3 (((1+s))^2)))-(2/(9 (1+s)))-(2/(3 (((2+s))^2)))+(22/(9 (2+s)))+((20 HarmonicNumber[s])/9)+(4/3) Zeta[2,1+s])+(cf^2) (-(1/(((1+s))^3))-(5/(1+s))-(1/(((2+s))^3))+(2/(((2+s))^2))+(5/(2+s))+((2 (EulerGamma+(1/(1+s))+PolyGamma[0,1+s]-(1+s) PolyGamma[1,2+s]))/(((1+s))^2))+((2 (EulerGamma+(1/(2+s))+PolyGamma[0,2+s]-(2+s) PolyGamma[1,3+s]))/(((2+s))^2))-4 (HarmonicNumber[s] PolyGamma[1,1+s]-(1/2) PolyGamma[2,1+s])+3 Zeta[2,1+s])+ca cf (-(1/(((1+s))^3))+(5/(6 (((1+s))^2)))+(53/(18 (1+s)))-(1/(((2+s))^3))+(5/(6 (((2+s))^2)))-(187/(18 (2+s)))+((Pi^2)/(6 (1+s)))+((Pi^2)/(6 (2+s)))-((67 HarmonicNumber[s])/9)+(1/3) (Pi^2) HarmonicNumber[s]-(11/3) Zeta[2,1+s]+2 Zeta[3,1+s]);
%/.s->1//N

ppsqq1=cf (-(ca/2)+cf) (-(2/(((1+s))^3))-(2/(((1+s))^2))+(4/(1+s))+((Pi^2)/(3 (1+s)))+(2/(((2+s))^3))-(2/(((2+s))^2))-(8/(2+s))-((Pi^2)/(3 (2+s)))+(5/(3+s))-(13/(9 (4+s)))+(25/(36 (5+s)))-(41/(100 (6+s)))+(4/(25 (7+s)))-HarmonicNumber[1+(s/2)]-(1/3) (Pi^2) (-HarmonicNumber[(1/2) (-1+s)]+HarmonicNumber[(s/2)])+HarmonicNumber[((1+s)/2)]+4 (-HarmonicNumber[(s/2)]+HarmonicNumber[((1+s)/2)])+(4/9) (-HarmonicNumber[1+(s/2)]+HarmonicNumber[((3+s)/2)])+(1/4) (-HarmonicNumber[2+(s/2)]+HarmonicNumber[((3+s)/2)])+(4/25) (-HarmonicNumber[2+(s/2)]+HarmonicNumber[((5+s)/2)])+(1/(((1+s))^3))(-8+(1+s) Log[16]+2 (1+s) PolyGamma[0,1+(s/2)]-2 (1+s) PolyGamma[0,((1+s)/2)]-(((1+s))^2) PolyGamma[1,1+(s/2)]+(((1+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((2+s))^3))0.9998400000000001` ((16/(((1+s))^2))+((12 s)/(((1+s))^2))+(2+s) Log[16]-2 (2+s) PolyGamma[0,1+(s/2)]+2 (2+s) PolyGamma[0,((1+s)/2)]+(((2+s))^2) PolyGamma[1,1+(s/2)]-(((2+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((3+s))^3))1.9702` ((164/((((1+s))^2) (((2+s))^2)))+((284 s)/((((1+s))^2) (((2+s))^2)))+((188 (s^2))/((((1+s))^2) (((2+s))^2)))+((60 (s^3))/((((1+s))^2) (((2+s))^2)))+((8 (s^4))/((((1+s))^2) (((2+s))^2)))-4 (3+s) Log[2]-2 (3+s) PolyGamma[0,1+(s/2)]+2 (3+s) PolyGamma[0,((1+s)/2)]+(((3+s))^2) PolyGamma[1,1+(s/2)]-(((3+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((4+s))^3))1.801` ((2176/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((4392 s)/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((3504 (s^2))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((1408 (s^3))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((288 (s^4))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((24 (s^5))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+4 (4+s) Log[2]-2 (4+s) PolyGamma[0,1+(s/2)]+2 (4+s) PolyGamma[0,((1+s)/2)]+(((4+s))^2) PolyGamma[1,1+(s/2)]-(((4+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((5+s))^3))1.3242` ((57328/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((146144 s)/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((162160 (s^2))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((103728 (s^3))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((42144 (s^4))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((11160 (s^5))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((1880 (s^6))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((184 (s^7))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((8 (s^8))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))-4 (5+s) Log[2]-2 (5+s) PolyGamma[0,1+(s/2)]+2 (5+s) PolyGamma[0,((1+s)/2)]+(((5+s))^2) PolyGamma[1,1+(s/2)]-(((5+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((6+s))^2))0.6348` (Log[16]-2 PolyGamma[0,4+(s/2)]+2 PolyGamma[0,((7+s)/2)]+(6+s) PolyGamma[1,4+(s/2)]-(6+s) PolyGamma[1,((7+s)/2)])+(1/(((7+s))^2))0.1398` (Log[16]+2 PolyGamma[0,4+(s/2)]-2 PolyGamma[0,((9+s)/2)]-(7+s) PolyGamma[1,4+(s/2)]+(7+s) PolyGamma[1,((9+s)/2)])+(1/2) (-Zeta[3,1+(s/2)]+Zeta[3,((1+s)/2)]));
%/.s->1//N

pqq1p=ppsqq1+pnsp1;

pqq1=cf tf ((40/(9 s))-(4/(((1+s))^3))-(8/(3 (((1+s))^2)))-(38/(9 (1+s)))-(4/(((2+s))^3))-(32/(3 (((2+s))^2)))+(130/(9 (2+s)))-(16/(3 (((3+s))^2)))-(112/(9 (3+s)))+((20 HarmonicNumber[s])/9)+(4/3) Zeta[2,1+s])+(cf^2) ((1/(((1+s))^3))-(2/(((1+s))^2))-(1/(1+s))-((π^2)/(3 (1+s)))-((2.99968`)/(((2+s))^3))+((8.28934175479506`)/(2+s))+((3.9404`)/(((3+s))^3))-((11.48105819700875`)/(3+s))-((3.602`)/(((4+s))^3))+((15.250136953231756`)/(4+s))+((2.6484`)/(((5+s))^3))-((14.225016715974174`)/(5+s))-((1.2696`)/(((6+s))^3))+((10.471812735714952`)/(6+s))+((0.2796`)/(((7+s))^3))-((5.776292409535209`)/(7+s))+((2.5480153333333333`)/(8+s))-((1.0411433333333333`)/(9+s))+((0.43270533333333333`)/(10+s))-((0.136518`)/(11+s))+((0.022368000000000002`)/(12+s))+(1/(((1+s))^3))(-8+(1+s) Log[16]+2 (1+s) PolyGamma[0,1+(s/2)]-2 (1+s) PolyGamma[0,((1+s)/2)]-(((1+s))^2) PolyGamma[1,1+(s/2)]+(((1+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((2+s))^3))0.9998400000000001` ((16/(((1+s))^2))+((12 s)/(((1+s))^2))+(2+s) Log[16]-2 (2+s) PolyGamma[0,1+(s/2)]+2 (2+s) PolyGamma[0,((1+s)/2)]+(((2+s))^2) PolyGamma[1,1+(s/2)]-(((2+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((3+s))^3))1.9702` ((164/((((1+s))^2) (((2+s))^2)))+((284 s)/((((1+s))^2) (((2+s))^2)))+((188 (s^2))/((((1+s))^2) (((2+s))^2)))+((60 (s^3))/((((1+s))^2) (((2+s))^2)))+((8 (s^4))/((((1+s))^2) (((2+s))^2)))-4 (3+s) Log[2]-2 (3+s) PolyGamma[0,1+(s/2)]+2 (3+s) PolyGamma[0,((1+s)/2)]+(((3+s))^2) PolyGamma[1,1+(s/2)]-(((3+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((4+s))^3))1.801` ((2176/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((4392 s)/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((3504 (s^2))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((1408 (s^3))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((288 (s^4))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((24 (s^5))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+4 (4+s) Log[2]-2 (4+s) PolyGamma[0,1+(s/2)]+2 (4+s) PolyGamma[0,((1+s)/2)]+(((4+s))^2) PolyGamma[1,1+(s/2)]-(((4+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((5+s))^3))1.3242` ((57328/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((146144 s)/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((162160 (s^2))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((103728 (s^3))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((42144 (s^4))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((11160 (s^5))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((1880 (s^6))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((184 (s^7))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((8 (s^8))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))-4 (5+s) Log[2]-2 (5+s) PolyGamma[0,1+(s/2)]+2 (5+s) PolyGamma[0,((1+s)/2)]+(((5+s))^2) PolyGamma[1,1+(s/2)]-(((5+s))^2) PolyGamma[1,((1+s)/2)])+((2 (EulerGamma+(1/(1+s))+PolyGamma[0,1+s]-(1+s) PolyGamma[1,2+s]))/(((1+s))^2))+((2 (EulerGamma+(1/(2+s))+PolyGamma[0,2+s]-(2+s) PolyGamma[1,3+s]))/(((2+s))^2))-(1/(((6+s))^2))0.6348` (Log[16]-2 PolyGamma[0,4+(s/2)]+2 PolyGamma[0,((7+s)/2)]+(6+s) PolyGamma[1,4+(s/2)]-(6+s) PolyGamma[1,((7+s)/2)])+(1/(((7+s))^2))0.1398` (Log[16]+2 PolyGamma[0,4+(s/2)]-2 PolyGamma[0,((9+s)/2)]-(7+s) PolyGamma[1,4+(s/2)]+(7+s) PolyGamma[1,((9+s)/2)])-4 (HarmonicNumber[s] PolyGamma[1,1+s]-(1/2) PolyGamma[2,1+s])+3 Zeta[2,1+s])+ca cf (-(2/(((1+s))^3))+(11/(6 (((1+s))^2)))+(17/(18 (1+s)))+((π^2)/(3 (1+s)))-((0.00015999999999993797`)/(((2+s))^3))+(11/(6 (((2+s))^2)))-((10.388625699438194`)/(2+s))-((1.9702`)/(((3+s))^3))+((5.740529098504375`)/(3+s))+((1.801`)/(((4+s))^3))-((7.625068476615878`)/(4+s))-((1.3242`)/(((5+s))^3))+((7.112508357987087`)/(5+s))+((0.6348`)/(((6+s))^3))-((5.235906367857476`)/(6+s))-((0.1398`)/(((7+s))^3))+((2.8881462047676045`)/(7+s))-((1.2740076666666666`)/(8+s))+((0.5205716666666667`)/(9+s))-((0.21635266666666667`)/(10+s))+((0.068259`)/(11+s))-((0.011184000000000001`)/(12+s))-((67 HarmonicNumber[s])/9)+(1/3) (π^2) HarmonicNumber[s]-(1/(2 (((1+s))^3)))(-8+(1+s) Log[16]+2 (1+s) PolyGamma[0,1+(s/2)]-2 (1+s) PolyGamma[0,((1+s)/2)]-(((1+s))^2) PolyGamma[1,1+(s/2)]+(((1+s))^2) PolyGamma[1,((1+s)/2)])+(1/(((2+s))^3))0.49992000000000003` ((16/(((1+s))^2))+((12 s)/(((1+s))^2))+(2+s) Log[16]-2 (2+s) PolyGamma[0,1+(s/2)]+2 (2+s) PolyGamma[0,((1+s)/2)]+(((2+s))^2) PolyGamma[1,1+(s/2)]-(((2+s))^2) PolyGamma[1,((1+s)/2)])+(1/(((3+s))^3))0.9851` ((164/((((1+s))^2) (((2+s))^2)))+((284 s)/((((1+s))^2) (((2+s))^2)))+((188 (s^2))/((((1+s))^2) (((2+s))^2)))+((60 (s^3))/((((1+s))^2) (((2+s))^2)))+((8 (s^4))/((((1+s))^2) (((2+s))^2)))-4 (3+s) Log[2]-2 (3+s) PolyGamma[0,1+(s/2)]+2 (3+s) PolyGamma[0,((1+s)/2)]+(((3+s))^2) PolyGamma[1,1+(s/2)]-(((3+s))^2) PolyGamma[1,((1+s)/2)])+(1/(((4+s))^3))0.9005` ((2176/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((4392 s)/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((3504 (s^2))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((1408 (s^3))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((288 (s^4))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((24 (s^5))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+4 (4+s) Log[2]-2 (4+s) PolyGamma[0,1+(s/2)]+2 (4+s) PolyGamma[0,((1+s)/2)]+(((4+s))^2) PolyGamma[1,1+(s/2)]-(((4+s))^2) PolyGamma[1,((1+s)/2)])+(1/(((5+s))^3))0.6621` ((57328/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((146144 s)/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((162160 (s^2))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((103728 (s^3))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((42144 (s^4))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((11160 (s^5))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((1880 (s^6))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((184 (s^7))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((8 (s^8))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))-4 (5+s) Log[2]-2 (5+s) PolyGamma[0,1+(s/2)]+2 (5+s) PolyGamma[0,((1+s)/2)]+(((5+s))^2) PolyGamma[1,1+(s/2)]-(((5+s))^2) PolyGamma[1,((1+s)/2)])+(1/(((6+s))^2))0.3174` (Log[16]-2 PolyGamma[0,4+(s/2)]+2 PolyGamma[0,((7+s)/2)]+(6+s) PolyGamma[1,4+(s/2)]-(6+s) PolyGamma[1,((7+s)/2)])-(1/(((7+s))^2))0.0699` (Log[16]+2 PolyGamma[0,4+(s/2)]-2 PolyGamma[0,((9+s)/2)]-(7+s) PolyGamma[1,4+(s/2)]+(7+s) PolyGamma[1,((9+s)/2)])-(11/3) Zeta[2,1+s]+2 Zeta[3,1+s]);
%/.s->1//N

pqg1=cf tf (-(2/(((1+s))^3))+(1/(((1+s))^2))+(14/(1+s))-((2 (Pi^2))/(3 (1+s)))+(4/(((2+s))^3))-(4/(((2+s))^2))-(29/(2+s))+((4 (Pi^2))/(3 (2+s)))+(20/(3+s))-((4 (Pi^2))/(3 (3+s)))+((4 HarmonicNumber[s])/(1+s))-((4 HarmonicNumber[1+s])/(1+s))-((8 HarmonicNumber[1+s])/(2+s))+((8 HarmonicNumber[2+s])/(3+s))+((2 ((Pi^2)+6 ((HarmonicNumber[s])^2)+6 PolyGamma[1,1+s]))/(6+6 s))-((4 ((Pi^2)+6 ((HarmonicNumber[1+s])^2)+6 PolyGamma[1,2+s]))/(12+6 s))+((4 ((Pi^2)+6 ((HarmonicNumber[2+s])^2)+6 PolyGamma[1,3+s]))/(18+6 s)))+ca tf ((40/(9 s))-(4/(((1+s))^3))-(2/(((1+s))^2))-(4/(1+s))-(8/(((2+s))^3))-(16/(((2+s))^2))+(54/(2+s))-((4 (Pi^2))/(3 (2+s)))-(88/(3 (((3+s))^2)))-(373/(9 (3+s)))+(58/(9 (4+s)))-(49/(36 (5+s)))+(247/(450 (6+s)))-(9/(50 (7+s)))+(8/(25 (8+s)))+((8 HarmonicNumber[2+s])/(2+s))-((8 HarmonicNumber[3+s])/(3+s))+(1/(((1+s))^3))(-8+(1+s) Log[16]+2 (1+s) PolyGamma[0,1+(s/2)]-2 (1+s) PolyGamma[0,((1+s)/2)]-(((1+s))^2) PolyGamma[1,1+(s/2)]+(((1+s))^2) PolyGamma[1,((1+s)/2)])+(1/(((2+s))^3))2 ((16/(((1+s))^2))+((12 s)/(((1+s))^2))+(2+s) Log[16]-2 (2+s) PolyGamma[0,1+(s/2)]+2 (2+s) PolyGamma[0,((1+s)/2)]+(((2+s))^2) PolyGamma[1,1+(s/2)]-(((2+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((3+s))^3))2 ((164/((((1+s))^2) (((2+s))^2)))+((284 s)/((((1+s))^2) (((2+s))^2)))+((188 (s^2))/((((1+s))^2) (((2+s))^2)))+((60 (s^3))/((((1+s))^2) (((2+s))^2)))+((8 (s^4))/((((1+s))^2) (((2+s))^2)))-4 (3+s) Log[2]-2 (3+s) PolyGamma[0,1+(s/2)]+2 (3+s) PolyGamma[0,((1+s)/2)]+(((3+s))^2) PolyGamma[1,1+(s/2)]-(((3+s))^2) PolyGamma[1,((1+s)/2)])-((2 ((Pi^2)+6 ((HarmonicNumber[1+s])^2)-6 PolyGamma[1,2+s]))/(6+6 s))+((4 ((Pi^2)+6 ((HarmonicNumber[2+s])^2)-6 PolyGamma[1,3+s]))/(12+6 s))-((4 ((Pi^2)+6 ((HarmonicNumber[3+s])^2)-6 PolyGamma[1,4+s]))/(18+6 s)));
%/.s->1//N

pgq1=cf tf (-(40/(9 s))+(40/(9 (1+s)))-(32/(9 (2+s)))+((8 HarmonicNumber[s])/(3 s))-((8 HarmonicNumber[1+s])/(3 (1+s)))+((4 HarmonicNumber[2+s])/(3 (2+s))))+(cf^2) (-(2/(((1+s))^3))-(2/(((1+s))^2))-(5/(2 (1+s)))+(1/(((2+s))^3))-(7/(2 (((2+s))^2)))-(7/(2 (2+s)))+((6 HarmonicNumber[s])/s)-((6 HarmonicNumber[1+s])/(1+s))+((5 HarmonicNumber[2+s])/(2+s))-(((π^2)+6 ((HarmonicNumber[s])^2)-6 PolyGamma[1,1+s])/(3 s))+((2 ((π^2)+6 ((HarmonicNumber[1+s])^2)-6 PolyGamma[1,2+s]))/(6+6 s))-(((π^2)+6 ((HarmonicNumber[2+s])^2)-6 PolyGamma[1,3+s])/(12+6 s)))+ca cf ((1/s)+(4/(((1+s))^3))+(12/(((1+s))^2))-(17/(9 (1+s)))+((2 (π^2))/(3 (1+s)))+(2/(((2+s))^3))+(5/(((2+s))^2))+(10/(9 (2+s)))+(8/(3 (((3+s))^2)))+(31/(9 (3+s)))+(11/(36 (4+s)))-(119/(900 (5+s)))-(7/(200 (6+s)))-(2/(25 (7+s)))-((22 HarmonicNumber[s])/(3 s))+((22 HarmonicNumber[1+s])/(3 (1+s)))-((17 HarmonicNumber[2+s])/(3 (2+s)))-(1/(s^2))(Log[16]-2 PolyGamma[0,1+(s/2)]+2 PolyGamma[0,((1+s)/2)]+s PolyGamma[1,1+(s/2)]-s PolyGamma[1,((1+s)/2)])-(1/(((1+s))^3))(-8+(1+s) Log[16]+2 (1+s) PolyGamma[0,1+(s/2)]-2 (1+s) PolyGamma[0,((1+s)/2)]-(((1+s))^2) PolyGamma[1,1+(s/2)]+(((1+s))^2) PolyGamma[1,((1+s)/2)])-(1/(2 (((2+s))^3)))((16/(((1+s))^2))+((12 s)/(((1+s))^2))+(2+s) Log[16]-2 (2+s) PolyGamma[0,1+(s/2)]+2 (2+s) PolyGamma[0,((1+s)/2)]+(((2+s))^2) PolyGamma[1,1+(s/2)]-(((2+s))^2) PolyGamma[1,((1+s)/2)])+(((π^2)+6 ((HarmonicNumber[s])^2)-6 PolyGamma[1,1+s])/(3 s))-((4 (1+EulerGamma s+s (PolyGamma[0,s]-s PolyGamma[1,1+s])))/(s^3))-((2 ((π^2)+6 ((HarmonicNumber[1+s])^2)-6 PolyGamma[1,2+s]))/(6+6 s))+((4 (EulerGamma+(1/(1+s))+PolyGamma[0,1+s]-(1+s) PolyGamma[1,2+s]))/(((1+s))^2))+(((π^2)+6 ((HarmonicNumber[2+s])^2)-6 PolyGamma[1,3+s])/(12+6 s))-((2 (EulerGamma+(1/(2+s))+PolyGamma[0,2+s]-(2+s) PolyGamma[1,3+s]))/(((2+s))^2)));
%/.s->1//N

pgg1=cf ((4/(3 s))-(4/(((1+s))^3))+(6/(((1+s))^2))-(16/(1+s))-(4/(((2+s))^3))+(10/(((2+s))^2))+(8/(2+s))+(20/(3 (3+s)))) tf+ca tf (-(46/(9 s))+(4/(3 (((1+s))^2)))+(58/(9 (1+s)))+(4/(3 (((2+s))^2)))-(38/(9 (2+s)))+(46/(9 (3+s)))+((20 HarmonicNumber[s])/9))+(ca^2) ((2/(((1+s))^3))+(25/(3 (((1+s))^2)))-(97/(18 (1+s)))+((π^2)/(1+s))+((6.00016`)/(((2+s))^3))-(11/(3 (((2+s))^2)))-((2.476082477613347`)/(2+s))-((π^2)/(3 (2+s)))-((2.0298`)/(((3+s))^3))+(44/(3 (((3+s))^2)))-((7.395105409252367`)/(3+s))+((π^2)/(3 (3+s)))-((1.801`)/(((4+s))^3))+((4.708401809949211`)/(4+s))+((1.3242`)/(((5+s))^3))-((6.564175024653755`)/(5+s))-((0.6348`)/(((6+s))^3))+((4.926461923413032`)/(6+s))+((0.1398`)/(((7+s))^3))-((2.8781462047676043`)/(7+s))+((1.1140076666666667`)/(8+s))-((0.5205716666666667`)/(9+s))+((0.21635266666666667`)/(10+s))-((0.068259`)/(11+s))+((0.011184000000000001`)/(12+s))-((67 HarmonicNumber[s])/9)+(1/3) (π^2) HarmonicNumber[s]-(1/(s^2))(Log[16]-2 PolyGamma[0,1+(s/2)]+2 PolyGamma[0,((1+s)/2)]+s PolyGamma[1,1+(s/2)]-s PolyGamma[1,((1+s)/2)])-(1/(((1+s))^3))(-8+(1+s) Log[16]+2 (1+s) PolyGamma[0,1+(s/2)]-2 (1+s) PolyGamma[0,((1+s)/2)]-(((1+s))^2) PolyGamma[1,1+(s/2)]+(((1+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((2+s))^3))1.99992` ((16/(((1+s))^2))+((12 s)/(((1+s))^2))+(2+s) Log[16]-2 (2+s) PolyGamma[0,1+(s/2)]+2 (2+s) PolyGamma[0,((1+s)/2)]+(((2+s))^2) PolyGamma[1,1+(s/2)]-(((2+s))^2) PolyGamma[1,((1+s)/2)])+(1/(((3+s))^3))0.014900000000000024` ((164/((((1+s))^2) (((2+s))^2)))+((284 s)/((((1+s))^2) (((2+s))^2)))+((188 (s^2))/((((1+s))^2) (((2+s))^2)))+((60 (s^3))/((((1+s))^2) (((2+s))^2)))+((8 (s^4))/((((1+s))^2) (((2+s))^2)))-4 (3+s) Log[2]-2 (3+s) PolyGamma[0,1+(s/2)]+2 (3+s) PolyGamma[0,((1+s)/2)]+(((3+s))^2) PolyGamma[1,1+(s/2)]-(((3+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((4+s))^3))0.9005` ((2176/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((4392 s)/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((3504 (s^2))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((1408 (s^3))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((288 (s^4))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+((24 (s^5))/((((1+s))^2) (((2+s))^2) (((3+s))^2)))+4 (4+s) Log[2]-2 (4+s) PolyGamma[0,1+(s/2)]+2 (4+s) PolyGamma[0,((1+s)/2)]+(((4+s))^2) PolyGamma[1,1+(s/2)]-(((4+s))^2) PolyGamma[1,((1+s)/2)])-(1/(((5+s))^3))0.6621` ((57328/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((146144 s)/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((162160 (s^2))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((103728 (s^3))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((42144 (s^4))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((11160 (s^5))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((1880 (s^6))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((184 (s^7))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))+((8 (s^8))/((((1+s))^2) (((2+s))^2) (((3+s))^2) (((4+s))^2)))-4 (5+s) Log[2]-2 (5+s) PolyGamma[0,1+(s/2)]+2 (5+s) PolyGamma[0,((1+s)/2)]+(((5+s))^2) PolyGamma[1,1+(s/2)]-(((5+s))^2) PolyGamma[1,((1+s)/2)])-((4 (1+EulerGamma s+s (PolyGamma[0,s]-s PolyGamma[1,1+s])))/(s^3))+((8 (EulerGamma+(1/(1+s))+PolyGamma[0,1+s]-(1+s) PolyGamma[1,2+s]))/(((1+s))^2))-((4 (EulerGamma+(1/(2+s))+PolyGamma[0,2+s]-(2+s) PolyGamma[1,3+s]))/(((2+s))^2))+((4 (EulerGamma+(1/(3+s))+PolyGamma[0,3+s]-(3+s) PolyGamma[1,4+s]))/(((3+s))^2))-(1/(((6+s))^2))0.3174` (Log[16]-2 PolyGamma[0,4+(s/2)]+2 PolyGamma[0,((7+s)/2)]+(6+s) PolyGamma[1,4+(s/2)]-(6+s) PolyGamma[1,((7+s)/2)])+(1/(((7+s))^2))0.0699` (Log[16]+2 PolyGamma[0,4+(s/2)]-2 PolyGamma[0,((9+s)/2)]-(7+s) PolyGamma[1,4+(s/2)]+(7+s) PolyGamma[1,((9+s)/2)])-4 (HarmonicNumber[s] PolyGamma[1,1+s]-(1/2) PolyGamma[2,1+s])+2 Zeta[3,1+s]);
%/.s->1//N

phif=pqq0+a0 pqq1;
phig=pgg0+a0 pgg1;
thetaf=pqg0+a0 pqg1;
thetag=pgq0+a0 pgq1;
t=ta;
g0=gn;
f0=Un+Dn+2 dbarPubarn+2 sbarn;

a0=0.025;
b1=10.7;
a1=0.025;

a11=((E^((1/2) t (-2 b1+phif+phig-(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) (b1 (a1 thetaf thetag (-phif-phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+a1 (E^(t (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))) thetaf thetag (phif+phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+(b1^2) (E^(b1 t)) (-(-1+(E^(t (Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) (phif-phig)-(Sqrt[(((phif-phig))^2)+4 thetaf thetag])-(E^(t (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))) (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+(E^(t (b1+(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) ((phif^3)+(phif^2) (-3 phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+((phig^2)-(-4+a1) thetaf thetag) (-phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+phif (3 (phig^2)+(4+a1) thetaf thetag-2 phig (Sqrt[(((phif-phig))^2)+4 thetaf thetag])))+(E^(b1 t)) (-(phif^3)+((phig^2)-(-4+a1) thetaf thetag) (phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+(phif^2) (3 phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))-phif (3 (phig^2)+(4+a1) thetaf thetag+2 phig (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))))+4 a1 (E^((1/2) t (b1+(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) ((Sqrt[(((phif-phig))^2)+4 thetaf thetag]) (-(b1^2) phif+phif (((phif-phig))^2)+(3 phif-phig) thetaf thetag) Cosh[(1/2) t (Sqrt[(((phif-phig))^2)+4 thetaf thetag])] Sinh[((b1 t)/2)]+((b1^2) thetaf thetag Cosh[((b1 t)/2)]+((phif^2)-phif phig+thetaf thetag) (-(b1^2)+(((phif-phig))^2)+4 thetaf thetag) Sinh[((b1 t)/2)]) Sinh[(1/2) t (Sqrt[(((phif-phig))^2)+4 thetaf thetag])])))/(2 b1 (Sqrt[(((phif-phig))^2)+4 thetaf thetag]) (-(b1^2)+(((phif-phig))^2)+4 thetaf thetag));

a12=((E^((1/2) t (-2 b1+phif+phig-(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) 
(b1 thetaf (-2 (b1^2) (E^(b1 t)) (-1+(E^(t (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))))+(E^(t (b1+(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) (2 (phif^2)-(4+a1) phif phig+(2+a1) (phig^2)+2 (4+a1) thetaf thetag-a1 phig (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))-(E^(b1 t)) (2 (phif^2)-(4+a1) phif phig+(2+a1) (phig^2)+2 (4+a1) thetaf thetag+a1 phig (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+a1 (-2 thetaf thetag+phig (phif-phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))+a1 (E^(t (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))) (2 thetaf thetag+phig (-phif+phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))))+4 a1 (E^((1/2) t (b1+(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) thetaf ((-(b1^2)+(phif^2)-phif phig+2 thetaf thetag) (Sqrt[(((phif-phig))^2)+4 thetaf thetag]) Cosh[(1/2) t (Sqrt[(((phif-phig))^2)+4 thetaf thetag])] Sinh[((b1 t)/2)]+((b1^2) phig Cosh[((b1 t)/2)]+phif (-(b1^2)+(((phif-phig))^2)+4 thetaf thetag) Sinh[((b1 t)/2)]) Sinh[(1/2) t (Sqrt[(((phif-phig))^2)+4 thetaf thetag])])))/(2 b1 (Sqrt[(((phif-phig))^2)+4 thetaf thetag]) (-(b1^2)+(((phif-phig))^2)+4 thetaf thetag));

a21=(2 (E^((1/2) (-b1+phif+phig) t)) thetag (-a1 ((b1+phif-phig) (b1+phig)-2 thetaf thetag) (Sqrt[(((phif-phig))^2)+4 thetaf thetag]) Cosh[(1/2) t (Sqrt[(((phif-phig))^2)+4 thetaf thetag])] Sinh[((b1 t)/2)]+(b1 (-(b1+phif-phig) (b1-(1+a1) phif+phig)+2 (2+a1) thetaf thetag) Cosh[((b1 t)/2)]-(b1+a1 phig) ((b1^2)-(((phif-phig))^2)-4 thetaf thetag) Sinh[((b1 t)/2)]) Sinh[(1/2) t (Sqrt[(((phif-phig))^2)+4 thetaf thetag])]))/(b1 (Sqrt[(((phif-phig))^2)+4 thetaf thetag]) (-(b1^2)+(((phif-phig))^2)+4 thetaf thetag));

a22=((E^((1/2) t (-2 b1+phif+phig-(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) (b1 (a1 thetaf thetag (-phif-phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+a1 (E^(t (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))) thetaf thetag (phif+phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+(b1^2) (E^(b1 t)) ((-1+(E^(t (Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) phif+phig-(Sqrt[(((phif-phig))^2)+4 thetaf thetag])-(E^(t (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))) (phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))+(E^(b1 t)) ((phif^3)-(phig^3)-(4+a1) phig thetaf thetag+(phig^2) (Sqrt[(((phif-phig))^2)+4 thetaf thetag])-(-4+a1) thetaf thetag (Sqrt[(((phif-phig))^2)+4 thetaf thetag])+(phif^2) (-3 phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+phif (3 (phig^2)-(-4+a1) thetaf thetag-2 phig (Sqrt[(((phif-phig))^2)+4 thetaf thetag])))+(E^(t (b1+(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) (-(phif^3)+(phig^3)+(4+a1) phig thetaf thetag+(phig^2) (Sqrt[(((phif-phig))^2)+4 thetaf thetag])-(-4+a1) thetaf thetag (Sqrt[(((phif-phig))^2)+4 thetaf thetag])+(phif^2) (3 phig+(Sqrt[(((phif-phig))^2)+4 thetaf thetag]))+phif (-3 (phig^2)+(-4+a1) thetaf thetag-2 phig (Sqrt[(((phif-phig))^2)+4 thetaf thetag]))))+4 a1 (E^((1/2) t (b1+(Sqrt[(((phif-phig))^2)+4 thetaf thetag])))) ((Sqrt[(((phif-phig))^2)+4 thetaf thetag]) (-(b1^2) phig+(((phif-phig))^2) phig-(phif-3 phig) thetaf thetag) Cosh[(1/2) t (Sqrt[(((phif-phig))^2)+4 thetaf thetag])] Sinh[((b1 t)/2)]+((b1^2) thetaf thetag Cosh[((b1 t)/2)]+((b1^2)-(((phif-phig))^2)-4 thetaf thetag) ((phif-phig) phig-thetaf thetag) Sinh[((b1 t)/2)]) Sinh[(1/2) t (Sqrt[(((phif-phig))^2)+4 thetaf thetag])])))/(2 b1 (Sqrt[(((phif-phig))^2)+4 thetaf thetag]) (-(b1^2)+(((phif-phig))^2)+4 thetaf thetag));

mnsNLO=Exp[   ta  (pqq0+ta2n/ta pnsp1)];
mnsNLOm=mnsNLO;
mnsNLOp=Exp[   ta  (pqq0+ta2n/ta pqq1p)];
uvn=mnsNLO Un;
dvn=mnsNLO Dn;

sgn=a11 f0+a12 g0;
gln=a21 f0+a22 g0;

m3n=m3i mnsNLOm;
m8n=m8i mnsNLOm;
van=vai mnsNLOp;
p3n=p3i mnsNLOp;
p8n=p8i mnsNLOp;
m15n=vai mnsNLOm;
p15n=sgi mnsNLOp;
m24n=van;
p24n=sgn;

bv=(van-m24n)*0.2;
cv=bv+(m24n-m15n)*.25;
sv=cv+(m15n-m8n)*1/3;
dv=sv+(m8n-m3n)*0.5;
uv=sv+(m8n+m3n)*0.5;

bp=(sgn-p24n)*0.2;
cp=bp+(p24n-p15n)*0.25;
sp=cp+(p15n-p8n)*1/3;
dp=sp+(p8n-p3n)*0.5;
up=sp+(p8n+p3n)*0.5;

pdfnp1=(uv);
pdfnp2=(dv);
pdfnp3=(sv);
pdfnp4=(cv);
pdfnp5=(bv);

pdfnm1=(up);
pdfnm2=(dp);
pdfnm3=(sp);
pdfnm4=(cp);
pdfnm5=(bp);

pdfnp0=gln;

g1=pdfnp0/.Q->20/.f->6/.lan->0.172;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[g1,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]] g1/.s->Alpha[[i]]/v],{i,1,M/2}],30]]
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[g1,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.0001,0.0009,0.00005}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[g1,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.001,0.009,0.0005}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[g1,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.01,0.09,0.005}]];
Parallelize[Table[{xx,  Re[NInverseLaplaceTransformBlock[g1,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.1,0.99,0.05}]];
Join[%%%%,%%%,%%,%]
xgalaplace=ListLogLinearPlot[%]

uva=pdfnp1/.Q->20/.f->6/.lan->0.172;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[  uva,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]] uva /.s->Alpha[[i]]/v],{i,1,M/2}],30]]
Parallelize[Table[{xx,Re[NInverseLaplaceTransformBlock[uva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.0001,0.0009,0.000025}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[uva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.001,0.009,0.00025}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[uva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.01,0.09,0.0025}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[uva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.1,0.99,0.025}]];
Join[%%%%,%%%,%%,%]
xuvalaplace=ListLogLinearPlot[%]

dva=pdfnp2/.Q->20/.f->6/.lan->0.172;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[dva,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]] dva/.s->Alpha[[i]]/v],{i,1,M/2}],30]]
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[dva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.0001,0.0009,0.000025}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[dva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.001,0.009,0.00025}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[dva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.01,0.09,0.0025}]];
Parallelize[Table[{xx,  Re[NInverseLaplaceTransformBlock[dva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.1,0.99,0.025}]];
Join[%%%%,%%%,%%,%]
xdvalaplace=ListLogLinearPlot[%]

ubar=pdfnm1/.Q->20/.f->5/.lan->0.172;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[ubar,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]]ubar/.s->Alpha[[i]]/v],{i,1,M/2}],30]]
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[ubar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.0001,0.0009,0.00005}]]
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[ubar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.001,0.009,0.0005}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[ubar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.01,0.09,0.005}]];
Parallelize[Table[{xx,  Re[NInverseLaplaceTransformBlock[ubar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.1,0.99,0.05}]];
Join[%%%%,%%%,%%,%]
xubaralaplace=ListLogLinearPlot[%]

here i use sigma for dbar

dbar=sgn/.Q->20/.f->5/.lan->0.172;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[dbar,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]]dbar/.s->Alpha[[i]]/v],{i,1,M/2}],30]]
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[dbar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.0001,0.0009,0.00005}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[dbar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.001,0.009,0.0005}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[dbar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.01,0.09,0.005}]];
Parallelize[Table[{xx,  Re[NInverseLaplaceTransformBlock[dbar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.1,0.99,0.05}]];
Join[%%%%,%%%,%%,%]
xdbaralaplace=ListLogLinearPlot[%]

dataxubarQ20={{0.00009999999747378748`,2.332464941903579`},{0.0001359355904561994`,2.189873904371344`},{0.0001847848521948135`,2.054939783902921`},{0.0002511883862501871`,1.927379677047144`},{0.000341454424632455`,1.806932465575796`},{0.0004641580999885655`,1.693363033439664`},{0.0006309560698090233`,1.58646136621202`},{0.0008576938806812954`,1.486044848467927`},{0.001165911270464204`,1.391960435777935`},{0.001584888409738539`,1.304086324642459`},{0.002154427472275366`,1.222340755703093`},{0.002928633779371603`,1.146691272669778`},{0.003981055720858419`,1.077169742857427`},{0.005411671737249519`,1.013891658781902`},{0.007356388115419393`,0.9570764652482618`},{0.009999949873565003`,0.9070573857105236`},{0.01359349124935502`,0.8642580380557255`},{0.018478393060226`,0.8290936865838824`},{0.02511871334778766`,0.8017434474392536`},{0.03414527216689742`,0.7817796810338169`},{0.04641557850550441`,0.7677722621863107`},{0.06309529229903935`,0.7572099930515691`},{0.08576896030347014`,0.7470226396276238`},{0.1165905455619902`,0.7337810352468981`},{0.1584880505295405`,0.7104842716899444`},{0.2154416727323648`,0.6592000936718958`},{0.2928619173157668`,0.5521171026777171`},{0.3981035865814762`,0.3769952345438137`},{0.5411644747178013`,0.1703963649663922`},{0.7356351426305391`,0.02603768298341192`},{0.9999899999999993`,2.587109210149607`*^-7}};
xubargjr=ListLogLinearPlot[dataxubarQ20,Joined->True,PlotStyle->{Red}]

Show[xubaralaplace,xubargjr]

dataxdbarQ20={{0.00009999999747378748`,2.322424308629712`},{0.0001359355904561994`,2.179185946230789`},{0.0001847848521948135`,2.043566285635781`},{0.0002511883862501871`,1.915277036458186`},{0.000341454424632455`,1.794049751195592`},{0.0004641580999885655`,1.679639318572211`},{0.0006309560698090233`,1.571821915048239`},{0.0008576938806812954`,1.470395492474589`},{0.001165911270464204`,1.375178942427773`},{0.001584888409738539`,1.286008732050021`},{0.002154427472275366`,1.20273937735689`},{0.002928633779371603`,1.125239268018279`},{0.003981055720858419`,1.053385066676805`},{0.005411671737249519`,0.987051907308446`},{0.007356388115419393`,0.9260985397429708`},{0.009999949873565003`,0.8703490119425801`},{0.01359349124935502`,0.8195743948900305`},{0.018478393060226`,0.7734829517401898`},{0.02511871334778766`,0.7317186195775454`},{0.03414527216689742`,0.6938069327931934`},{0.04641557850550441`,0.6588467430562985`},{0.06309529229903935`,0.6245597762284965`},{0.08576896030347014`,0.5855118149304195`},{0.1165905455619902`,0.5318478370433178`},{0.1584880505295405`,0.4525841810650438`},{0.2154416727323648`,0.3458182072070467`},{0.2928619173157668`,0.2257489435991472`},{0.3981035865814762`,0.114168298245298`},{0.5411644747178013`,0.03378796865276799`},{0.7356351426305391`,0.002289567115838124`},{0.9999899999999993`,4.627491987271922`*^-8}};
xdbargjr=ListLogLinearPlot[dataxdbarQ20,Joined->True,PlotStyle->{Red}]

Show[xdbaralaplace,xdbargjr]

dataxgQ20={{0.00009999999747378748`,23.892393335879`},{0.0001359355904561994`,22.26732697632169`},{0.0001847848521948135`,20.72848179868015`},{0.0002511883862501871`,19.27168039620026`},{0.000341454424632455`,17.89283773380725`},{0.0004641580999885655`,16.5879867805196`},{0.0006309560698090233`,15.3532362259752`},{0.0008576938806812954`,14.18474964275206`},{0.001165911270464204`,13.07870043116651`},{0.001584888409738539`,12.03118668031792`},{0.002154427472275366`,11.03818130252021`},{0.002928633779371603`,10.09542636865993`},{0.003981055720858419`,9.19832499903994`},{0.005411671737249519`,8.341827386357123`},{0.007356388115419393`,7.520341054892704`},{0.009999949873565003`,6.727720886371779`},{0.01359349124935502`,5.9574354635312`},{0.018478393060226`,5.203057942949918`},{0.02511871334778766`,4.459285509456372`},{0.03414527216689742`,3.723702803428695`},{0.04641557850550441`,2.999380848759284`},{0.06309529229903935`,2.298002474929072`},{0.08576896030347014`,1.642343411051629`},{0.1165905455619902`,1.065678316255441`},{0.1584880505295405`,0.6048493088214315`},{0.2154416727323648`,0.2855213620308811`},{0.2928619173157668`,0.1050799935389042`},{0.3981035865814762`,0.02790735040182798`},{0.5411644747178013`,0.004646139294468587`},{0.7356351426305391`,0.0002350391865875615`},{0.9999899999999993`,4.210242363413015`*^-9}};
xggjr=ListLogLinearPlot[dataxgQ20,Joined->True,PlotStyle->{Red}]

Show[xgalaplace,xggjr]

dataxuvQ20={{0.00009999999747378748`,0.02568128941970363`},{0.0001359355904561994`,0.02853608053542271`},{0.0001847848521948135`,0.03175146800692856`},{0.0002511883862501871`,0.03538420366578518`},{0.000341454424632455`,0.03950279427177846`},{0.0004641580999885655`,0.04419040770483322`},{0.0006309560698090233`,0.04954877386584543`},{0.0008576938806812954`,0.0557030973552638`},{0.001165911270464204`,0.06280844076718063`},{0.001584888409738539`,0.07105809746584951`},{0.002154427472275366`,0.0806939341605073`},{0.002928633779371603`,0.09201960024700452`},{0.003981055720858419`,0.1054165900844767`},{0.005411671737249519`,0.1213630376637192`},{0.007356388115419393`,0.1404538743116297`},{0.009999949873565003`,0.1634185556019968`},{0.01359349124935502`,0.191127958509929`},{0.018478393060226`,0.2245733296902461`},{0.02511871334778766`,0.2647840218934645`},{0.03414527216689742`,0.3126254882812256`},{0.04641557850550441`,0.3683799841786462`},{0.06309529229903935`,0.4309658754614485`},{0.08576896030347014`,0.4966259997605204`},{0.1165905455619902`,0.5570045007990219`},{0.1584880505295405`,0.5969655592167528`},{0.2154416727323648`,0.5937336370984354`},{0.2928619173157668`,0.5214554670661575`},{0.3981035865814762`,0.3683013863404659`},{0.5411644747178013`,0.1695482631857329`},{0.7356351426305391`,0.02603158641133319`},{0.9999899999999993`,2.581972059214556`*^-7}};
xuvgjr=ListLogLinearPlot[dataxuvQ20,Joined->True,PlotStyle->{Red}]

Show[xuvalaplace,xuvgjr]

dataxdvQ20={{0.00009999999747378748`,0.01528848861393844`},{0.0001359355904561994`,0.01739273821729706`},{0.0001847848521948135`,0.01978540132693457`},{0.0002511883862501871`,0.02250589316930883`},{0.000341454424632455`,0.0255991767878418`},{0.0004641580999885655`,0.0291165582410185`},{0.0006309560698090233`,0.03311674850295486`},{0.0008576938806812954`,0.03766708553637342`},{0.001165911270464204`,0.04284507536916078`},{0.001584888409738539`,0.04874046148985995`},{0.002154427472275366`,0.05545755859353824`},{0.002928633779371603`,0.06311833012766119`},{0.003981055720858419`,0.07186598451717241`},{0.005411671737249519`,0.08186895893314997`},{0.007356388115419393`,0.0933244674712255`},{0.009999949873565003`,0.1064595136730244`},{0.01359349124935502`,0.1215249782883448`},{0.018478393060226`,0.1387729071692778`},{0.02511871334778766`,0.1583987111979198`},{0.03414527216689742`,0.1804152293592115`},{0.04641557850550441`,0.2044056730409596`},{0.06309529229903935`,0.2290855424180304`},{0.08576896030347014`,0.2516213466045413`},{0.1165905455619902`,0.266790339081794`},{0.1584880505295405`,0.2664851546268451`},{0.2154416727323648`,0.2409471868395502`},{0.2928619173157668`,0.1841392271489105`},{0.3981035865814762`,0.1044992232420646`},{0.5411644747178013`,0.03293003026013149`},{0.7356351426305391`,0.002283469915853623`},{0.9999899999999993`,4.636429291535055`*^-8}};
xdvgjr=ListLogLinearPlot[dataxdvQ20,Joined->True,PlotStyle->{Red}]

Show[xdvgjr,xdvalaplace]

Needs["ErrorBarLogPlots`"]

cq=cf (-9-((2 (π^2))/3)-(2/(((1+s))^2))+(6/(1+s))-(2/(((2+s))^2))+(4/(2+s))+3 HarmonicNumber[s]+((2 HarmonicNumber[1+s])/(1+s))+((2 HarmonicNumber[2+s])/(2+s))+(1/3) ((π^2)+6 ((HarmonicNumber[s])^2)-6 PolyGamma[1,1+s])+4 Zeta[2,1+s]);
cg=f ((2/(((1+s))^2))-(2/(1+s))-(4/(((2+s))^2))+(16/(2+s))+(4/(((3+s))^2))-(16/(3+s))-((2 HarmonicNumber[1+s])/(1+s))+((4 HarmonicNumber[2+s])/(2+s))-((4 HarmonicNumber[3+s])/(3+s)));

sentenses1=4/9 (pdfnm1)(1+taQ cq/(4 Pi))/.Q->13.397/.f->6;
sentenses2=1/9 (pdfnm1)(1+taQ cq/(4 Pi))/.Q->13.397/.f->6;
sentenses3=2 1/9 (pdfnm3)(1+taQ cq/(4 Pi))/.Q->13.397/.f->5;
sentenses4=1/3(1/9+1/9+4/9)(pdfnp0)taQ cg/(4 Pi)/.Q->13.397/.f->6;
F2p=sentenses1+sentenses2+sentenses3+sentenses4  ;

xsixmaQ20={{0.00009999999747378748`,6.464803294632632`},{0.0001359355904561994`,6.059858360254181`},{0.0001847848521948135`,5.676083588448209`},{0.0002511883862501871`,5.312642819334331`},{0.000341454424632455`,4.968749338060361`},{0.0004641580999885655`,4.643674947214473`},{0.0006309560698090233`,4.336743489237493`},{0.0008576938806812954`,4.047332026511209`},{0.001165911270464204`,3.774869405597463`},{0.001584888409738539`,3.518829841985015`},{0.002154427472275366`,3.278741713525593`},{0.002928633779371603`,3.054190027193097`},{0.003981055720858419`,2.844825393593168`},{0.005411671737249519`,2.650374572227269`},{0.007356388115419393`,2.470649087427519`},{0.009999949873565003`,2.30554199568798`},{0.01359349124935502`,2.154992918470668`},{0.018478393060226`,2.018885906012665`},{0.02511871334778766`,1.896824037441736`},{0.03414527216689742`,1.787704897223782`},{0.04641557850550441`,1.689018171984635`},{0.06309529229903935`,1.595842943115106`},{0.08576896030347014`,1.499698066894163`},{0.1165905455619902`,1.387754498170538`},{0.1584880505295405`,1.243408206322666`},{0.2154416727323648`,1.049599141526704`},{0.2928619173157668`,0.7964614725632737`},{0.3981035865814762`,0.4958431726420474`},{0.5411644747178013`,0.2046185953914718`},{0.7356351426305391`,0.02833041143306138`},{0.9999899999999993`,3.050937785897188`*^-7}};
xsixmaQ20jgr=ListLogLinearPlot[xsixmaQ20,Joined->True,PlotStyle->{Red}]

Show[xdbaralaplace,xsixmaQ20jgr]