LerchPhi
Usage Message: LerchPhi[z, s, a] gives the Lerch transcendent Phi(z, s, a). Attributes[LerchPhi] = {Listable, NumericFunction, Protected} Options: DoublyInfinite
-> False IncludeSingularTerm
-> False Related Symbols: Zeta
Notes: Numerical evaluation of LerchPhi[z, s, a] is based on the definition
Sum[z^k/((a + k)^2)^(s/2), {k, 0, Infinity}]
Most references for this function use a different definition:
Sum[z^k/(a + k)^s, {k, 0, Infinity}]
The definition that is used in Mathematica was chosen because it is believed to have a more convenient branch cut structure for modern uses of this function. Although this definition has been widely discussed by experts on special functions, we are not aware of a published reference for this definition. Known Bugs: The documentation for LerchPhi[z, s, a], and some functions in Mathematica, use the definition
Sum[z^k/(a + k)^s, {k, 0, Infinity}]
This definition is in disagreement with the definition that is used for computing numerical values of LerchPhi[z, s, a].
Additional Online Documentation:
Mathematica 3.0
http://documents.wolfram.com/v3/RefGuide/LerchPhi.html
Mathematica 4.0
http://documents.wolfram.com/v4/RefGuide/LerchPhi.html
Questions or comments? Send email to support@wolfram.com.
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