where the terms with i + a = 0 are excluded.
The Lerch transcendent Φ(x1,
x2, a) is a generalization of the polylogarithm
(regarding x1) and the (generalized) zeta function
Many infinite sums (of reciprocal powers) can expressed as a Lerch transcendent, for
instance the Catalan beta function.
The function is also related to integrals of the Fermi-Dirac
distribution. And it is used to evaluate some series in number theory (Dirichlet