How does Mathematica calculate
Series[HypergeometricPFQ[{...},{...},z],{z, Infinity, *integer*}]
the asymptotic expression at infinity for generalized hypergeometric functions (GHF)?
For some parameters plugged in {…},{…} there are identities like GHF[z] = Exp[z] f[z] where f is a function that does not diverge for large z and so the answer for the question above is, it can be written as
Series[ GHF[z] ] = Exp[z] Series[ f[z] ] .
But since Mathematica is able to calculate the series for all parameters in {…},{…} I’ve tried I wondered have I missed an identity like above I can use for all GHF or is the series calculated in an entirely different way?