HurwitzLerchPhi[z, s, a]
gives the Hurwitz-Lerch transcendent .


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The Hurwitz-Lerch transcendent is defined as an analytic continuation of .
  • HurwitzLerchPhi is identical to LerchPhi for .
  • Unlike LerchPhi, HurwitzLerchPhi has singularities at for non-negative integers .
  • HurwitzLerchPhi has branch cut discontinuities in the complex plane running from to , and in the complex plane running from to .
  • For certain special arguments, HurwitzLerchPhi automatically evaluates to exact values.
  • HurwitzLerchPhi can be evaluated to arbitrary numerical precision.
  • HurwitzLerchPhi automatically threads over lists.
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