FeynCalc manual (development version)

HypExplicit

HypExplicit[exp, nu] expresses Hypergeometric functions in exp by their definition in terms of a sum (the Sum is omitted and nu is the summation index).

See also

Overview, HypergeometricIR.

Examples

Hypergeometric2F1[a, b, c, z] 
 
HypExplicit[%, \[Nu]]

\, _2F_1(a,b;c;z)

Γ(c)zνΓ(a+ν)Γ(b+ν)Γ(a)Γ(b)Γ(ν+1)Γ(c+ν)\frac{\Gamma (c) z^{\nu } \Gamma (a+\nu ) \Gamma (b+\nu )}{\Gamma (a) \Gamma (b) \Gamma (\nu +1) \Gamma (c+\nu )}

HypergeometricPFQ[{a, b, c}, {d, e}, z] 
 
HypExplicit[%, \[Nu]]

\, _3F_2(a,b,c;d,e;z)

Γ(d)Γ(e)zνΓ(a+ν)Γ(b+ν)Γ(c+ν)Γ(a)Γ(b)Γ(c)Γ(ν+1)Γ(d+ν)Γ(e+ν)\frac{\Gamma (d) \Gamma (e) z^{\nu } \Gamma (a+\nu ) \Gamma (b+\nu ) \Gamma (c+\nu )}{\Gamma (a) \Gamma (b) \Gamma (c) \Gamma (\nu +1) \Gamma (d+\nu ) \Gamma (e+\nu )}