@article{
author = "Cvijović, Đurđe",
year = "2010",
abstract = "It is known that the Lerch (or periodic) zeta function of non-positive integer order, l(-n)(xi), n is an element of N(0) := {0, 1, 2, 3, ...}, is a polynomial in cot(pi xi) of degree n+1. In this paper, a very simple explicit closed-form formula for this polynomial valid for any degree is derived. In addition, novel analogous explicit closed-form formulae for the Legendre chi function, the alternating Lerch zeta. function and the alternating Legendre chi function are established. The obtained formulae involve the Carlitz-Scoville tangent and secant numbers of higher order, and the derivative polynomials for tangent and secant are used in their derivation. Several special cases and consequences are pointed out, and some examples arc, also given.",
journal = "Proceedings of the American Mathematical Society",
title = "The Lerch Zeta and Related Functions of Non-Positive Integer Order",
volume = "138",
number = "3",
pages = "827-836",
doi = "10.1090/S0002-9939-09-10116-8"
}