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Asymptotics of generalized hypergeometric function

Posted 1 year ago

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?

POSTED BY: Luis Filsinger
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