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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 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.
Evaluate numerically:
Evaluate for complex arguments:
Evaluate to arbitrary precision:
The precision of the output tracks the precision of the input:
Simple exact values are generated automatically:
HurwitzLerchPhi threads element-wise over lists:
TraditionalForm formatting:
Moment and central moment of geometric distribution can be expressed using HurwitzLerchPhi:
Some hypergeometric functions can be expressed in terms of HurwitzLerchPhi:
Sum can generate HurwitzLerchPhi:
HurwitzLerchPhi differs from LerchPhi by a different choice of branch cut:
HurwitzLerchPhi includes singular terms, unlike LerchPhi:
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