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LerchPhi
LerchPhi[
z
,
s
,
a
] gives the Lerch transcendent  .
Mathematical function (see Section A.3.10).
 , where any term with  is excluded.
LerchPhi[
z
,
s
,
a
,
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`.
Further Examples
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Here we use the option  .
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LerchPhi satisfies an analog to the functional equation for the Zeta function.
In[3]:= 
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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,
a].
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If there is no singular term the option has no effect.
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This is a series expansion around  .
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