
where the terms with i + a = 0 are excluded. The Lerch transcendent Φ(x_{1}, x_{2}, a) is a generalization of the polylogarithm (regarding x_{1}) and the (generalized) zeta function (regarding x_{2}). Many infinite sums (of reciprocal powers) can expressed as a Lerch transcendent, for
instance the Catalan beta function. 