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2010•International Journal of Number TheoryRequires access

HYPERGEOMETRIC ZETA FUNCTIONS

Abdul Hassen, Hiêú D. Nguyêñ

Open publisher page 31 citations

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.

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What this paper is about

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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OpenAlex reports 31 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Mathematics, Generalized hypergeometric function, Arithmetic zeta function, Riemann zeta function, Hypergeometric function of a matrix argument, Basic hypergeometric series, Hypergeometric distribution, Hypergeometric function

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