by where is the Pochhammer symbol. Series at a = −n is given by A special case for n = 0 has the following series where is the polylogarithm. An asymptotic series for for and for An asymptotic series in the incomplete gamma function for The representation as a generalized hypergeometric function is Asymptotic expansion The polylogarithm function is defined as Let For and , an asymptotic expansion of for large and fixed and is given by for , where is the Pochhammer symbol. Let Let be its Taylor coefficients at . Then for fixed and , as . Software The Lerch transcendent is implemented as LerchPhi in Maple and Mathematica, and as lerchphi in mpmath and SymPy. References . . (See § 1.11, "The function Ψ(z,s,v)", p. 27) . (Includes various basic identities in the introduction.) . . . External links . Ramunas Garunkstis, Home Page (2005) (Provides numerous references and preprints.) Zeta and L-functions