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.
Examplesopen allclose all
Basic Examples (7)
Series expansion at Infinity:
Numerical Evaluation (4)
Specific Values (5)
Function Properties (5)
Series Expansions (1)
Find the Taylor expansion using Series:
Moment and central moment of geometric distribution can be expressed using HurwitzLerchPhi:
Properties & Relations (2)
Introduced in 2008