HYPERGEOMETRIC ZETA FUNCTIONS

Abdul Hassen, Hiêú D. Nguyêñ

Type: Article

Publication Date: 2010-02-01

Citations: 32

DOI: https://doi.org/10.1142/s179304211000282x

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.

Locations

International Journal of Number Theory - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (10)

Action	Title	Year	Authors
+ PDF Chat	Numbers generated by the reciprocal of 𝑒^{𝑥}-𝑥-1	1977	F. T. Howard
+	Introduction to the Theory of Entire Functions	1973	A. S. B. Holland
+	Riemann Zeta Function	2009	Dorin Ghişa
+	A sequence of numbers related to the exponential function	1967	F. T. Howard
+	Numbers Generated by the Reciprocal of e x - x - 1	1977	F. T. Howard
+	Some sequences of rational numbers related to the exponential function	1967	F. T. Howard
+	HYPERGEOMETRIC BERNOULLI POLYNOMIALS AND APPELL SEQUENCES	2008	Abdul Hassen Hiêú D. Nguyêñ
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown
+	Bernoulli numbers and confluent hypergeometric functions	2002	Karl Dilcher
+	THE ERROR ZETA FUNCTION	2007	Abdul Hassen Hiêú D. Nguyêñ