The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is classically defined by Φ(z, s, a) congruent sum_(k = 0)^∞ z^k/(a + k)^s, for left bracketing bar z right bracketing bar <1 and a!=0, -1, .... It is implemented in this form as HurwitzLerchPhi[z, s, a] in the Wolfram Language.

Bose-Einstein distribution | Dirichlet beta function | Dirichlet L-series | Fermi-Dirac distribution | Hurwitz zeta function | Jacobi theta functions | Legendre's chi-function | polylogarithm | unit square integral