Riemann's Zeta Function: The alternating Xi-Function Xia(s)
Abstract
As well known, the study of Riemanns zeta function ζ(s) involves the related entire function (s). A close relative of ζ(s) is the alternating zeta function η(s). Similar to ζ(s), also η(s) has a corresponding entire function a (s). After establishing its definition and a related functional equation, formulas based on incomplete gamma functions are worked out, allowing to numerically evaluate a (s). Examples verifying the obtained formulas are included.
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