Riemann's Zeta Function: The alternating Xi-Function Xia(s)
Number Theory
2016-10-24 v2
Abstract
As well known, the study of Riemanns zeta function {\zeta}(s) involves the related entire function {\xi}(s). A close relative of {\zeta}(s) is the alternating zeta function {\eta}(s). Similar to {\zeta}(s), also {\eta}(s) has a corresponding entire function {\xi}_a (s). After establishing its definition and a related functional equation, formulas based on incomplete gamma functions are worked out, allowing to numerically evaluate {\xi}_a (s). Examples verifying the obtained formulas are included.
Cite
@article{arxiv.1610.04344,
title = {Riemann's Zeta Function: The alternating Xi-Function Xia(s)},
author = {Renaat Van Malderen},
journal= {arXiv preprint arXiv:1610.04344},
year = {2016}
}