LerchPhi

LerchPhi[z,s,a]

gives the Lerch transcendent Φ(z,s,a).

Details and Options

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • .
  • For , the definition used is , where any term with is excluded.
  • LerchPhi[z,s,a,DoublyInfinite->True] gives the sum .
  • LerchPhi is a generalization of Zeta and PolyLog.
  • For certain special arguments, LerchPhi automatically evaluates to exact values.
  • LerchPhi can be evaluated to arbitrary numerical precision.
  • LerchPhi automatically threads over lists.

Examples

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Basic Examples  (3)

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Scope  (7)

Generalizations & Extensions  (2)

Options  (4)

Applications  (2)

Properties & Relations  (2)

Possible Issues  (5)

See Also

Zeta  PolyLog  HurwitzLerchPhi

Tutorials

Introduced in 1988
(1.0)