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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.

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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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