Four Variants of Riemann Zeta Function

By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in closed form, which shows remarkably that the...

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Bibliographic Details
Published in:Mathematics
Main Authors: Nadia N. Li, Wenchang Chu
Format: Article
Language:English
Published: MDPI AG 2022-08-01
Subjects:
Riemann zeta function
the gamma function
generating function
trigonometric function
bilateral hypergeometric series
Online Access:https://www.mdpi.com/2227-7390/10/16/2992
Description
Summary:By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in closed form, which shows remarkably that the values of these series result in multiples of integer powers of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> either by rational numbers or by algebraic numbers.
ISSN:2227-7390

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