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LerchPhi

LerchPhi[z, s, a]
gives the Lerch transcendent CapitalPhi(z, s, a).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Phi(z,s,a)=sum_(k=0)^(infty)z^k/(k+a)^s.
  • For Re(a)<0, the definition used is Phi(z,s,a)=sum_(k=0)^(infty)z^k((k+a)^2)^(-s/2), where any term with k+a=0 is excluded.
  • For certain special arguments, LerchPhi automatically evaluates to exact values.
  • LerchPhi can be evaluated to arbitrary numerical precision.
  • LerchPhi automatically threads over lists.
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