hep-ph 9706430

(*   LO    *)

mz=91.1887;
mb=4.3;
 β0=((1/4))*(11-((2*f)/3));
L[Q_]:=Log[(Q/(Λ^2))];
αsLO[Q_,f_]=(Pi/(β0*L[Q]));
AsLO[Q_,f_]=((αsLO[Q,f])/Pi);

Lh=Log[(Q/(mb^2))];

AsMachLO[Q_,f_]=AsLO[Q,f+1](1-AsLO[Q,f+1]*(Lh/6));
αsMachLO[Q_,f_]=AsMachLO[Q,f]*Pi;

αsMachLO[mz^2,4]/.Λ->.196

(*   NLO    *)

mz=91.1887;
mb=4.3;
 β0=((1/4))*(11-((2*f)/3));
β1=((1/(4^2)))*(102-((38*f)/3));

L[Q_]:=Log[(Q/(Λ^2))];
αsNLO[Q_,f_]=Pi((1/(β0*L[Q]))-((β1*Log[L[Q]])/(((β0)^3)*(((L[Q]))^2))));
AsNLO[Q_,f_]=((αsNLO[Q,f])/Pi);

Lh=Log[(Q/(mb^2))];

AsMachNLO[Q_,f_]=AsNLO[Q,f+1](1-AsNLO[Q,f+1]*(Lh/6)+(((AsNLO[Q,f+1]))^2)*
(((Lh^2)/36)-((19*Lh)/24)-(7/24)));
αsMachNLO[Q_,f_]=AsMachNLO[Q,f]*Pi;

αsMachNLO[mz^2,4]/.Λ->0.2959770960545159+0.019
αsMachNLO[mz^2,4]/.Λ->0.2959770960545159
%%-%

(*   NNLO    *)

mz=91.1887;
mb=4.3;
 β0=((1/4))*(11-((2*f)/3));
β1=((1/(4^2)))*(102-((38*f)/3));
β2=((1/(4^3)))*((2857/2)-((5033*f)/18)+((325*(f^2))/54));

L[Q_]:=Log[(Q/(Λ^2))];
AsNNLOOLD[Q_,f_]=(1/(β0*L[Q]))-((β1*Log[L[Q]])/(β0*(((β0*L[Q]))^2)))+(1/(((β0*L[Q]))^3))*((((β1)^2)/((β0)^2))*(Log[Log[L[Q]]]-Log[L[Q]]-1)+((β2)/(β0)));
AsNNLO[Q_,f_]=(1/(β0*L[Q]))-((β1*Log[L[Q]])/(β0*(((β0*L[Q]))^2)))+(1/(((β0*L[Q]))^3))*((((β1)^2)/((β0)^2))*(Log[L[Q]]^2-Log[L[Q]]-1)+((β2)/(β0)));

Lh=Log[(Q/(mb^2))];
cm3=-(80507/27648)*Zeta[3]-(2/3)*Zeta[2]*((1/3)*Log[2]+1)-(58933/124416)+(f/9)*(Zeta[2]+(2479/3456));

AsMachNNLO[Q_,f_]=AsNNLO[Q,f+1](1-AsNNLO[Q,f+1]*(Lh/6)+(((AsNNLO[Q,f+1]))^2)*
(((Lh^2)/36)-((19*Lh)/24)-(7/24))+
(((AsNNLO[Q,f+1]))^3)*(-((Lh^3)/216)-(131/576)*(Lh^2)+(Lh/1728)*(-8521+409*f)+cm3)
);
αsMachNNLO[Q_,f_]=AsMachNNLO[Q,f]*Pi;

αsMachNNLO[mz^2,4]/.Λ->0.289999999938901+4.8286950233149698^-003
αsMachNNLO[mz^2,4]/.Λ->0.289999999938901
%%-%