Hypergeometric Zeta Functions

Details Hypergeometric Zeta Functions Hypergeometric Zeta Functions

2005-09-27

arxiv.org/abs/math/0509637v1

Mathematics

Number Theory

23 pages, 3 figures, 2 tables

Scientific paper

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.

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