Hypergeometric-like Representation of the Zeta-Function of Riemann

2001/05/04 by Krzysztof Maslanka, Maslanka, Krzysztof · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0105007

arxiv created 2001/05/04 · arxiv updated 2009/11/30

Abstract

We present a new expansion of the zeta-function of Riemann. The current formalism -- which combines both the idea of interpolation with constraints and the concept of hypergeometric functions -- can, in a natural way, be generalised within the theory of the zeta-function of Hawking offering thus a variety of applications in quantum field theory, quantum cosmology and statistical mechanics.

Cited by

• A new expansion of the Riemann zeta function

Related

• Hypergeometric Zeta Functions
• On Maslanka's representation for the Riemann zeta-function
• Two New Zeta Constants: Fractal String, Continued Fraction, and Hypergeometric Aspects of the Riemann Zeta Function
• On the use of the variable change w=exp(u) to establish novel integral representations of the Riemann zeta(s,a) -function, incomplete gamma- function, confluent hypergeometric Phi-function and beta function
• Concerning Riemann Hypothesis