] gives the Lerch transcendent .
Mathematical function (see Section A.3.10).
, where any term with is excluded.
DoublyInfinite->True] gives the sum .
LerchPhi is a generalization of Zeta and PolyLog.
See the Mathematica book: Section 3.2.10.
Related package: NumberTheory`Ramanujan`.
Here we use the option .
LerchPhi satisfies an analog to the functional equation for the Zeta function.
The usual notation for a sum that excludes a particular term is , as, for example, in the definitions of the invariants and in terms of the half-periods \[Omega] and . Mathematica simply allows you to choose whether or not to include the singular term (if there is one) in the series for Zeta[s,
a] and LerchPhi[z, s,
If there is no singular term the option has no effect.
This is a series expansion around .
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