Hypergeometric zeta functions

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Abstract

This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties analogous to their classical counterpart, including the intimate connection to Bernoulli numbers. These new properties are treated in detail and are used to demonstrate a functional inequality satisfied by second-order hypergeometric zeta functions.

Original languageEnglish (US)
Pages (from-to)99-126
Number of pages28
JournalInternational Journal of Number Theory
Volume6
Issue number1
DOIs
StatePublished - Feb 2010

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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