Research ArticleOpen AccessGoogle Scholar indexed
The Infinite Polynomial Products of the Gamma and Zeta Functions
Independent Researcher, Kékkút, Hungary
Independent Researcher, Kékkút, Hungary
- 1 Independent Researcher, Kékkút, Hungary
- 2 Independent Researcher, Kékkút, Hungary
Advances in Pure Mathematics·Volume 12 (2022)·Pages 451–464·Published 22 June 2022·DOI10.4236/apm.2022.126034
Copy link · social · email
Abstract
Starting with the binomial coefficient and using its infinite product representation, the infinite product representation of the gamma function and of the zeta function are composed of an exponential and of a trigonometric component and proved. It is proved, that all these components define imaginary roots on the critical line, if written in the form as they are in the functional equation of the zeta function.
KeywordsGamma FunctionZeta FunctionCritical Line
- Titmarsh, E.C. and Heath-Brown, D.R. (1994) The Theorie of the Riemann Zeta- Function. 2nd Edition, Oxford University Press, Oxford.
- Martinez, J. (2022) On the Absence of Zeros of Riemann Zeta-Function Out of R(z) = 1/2. Advances in Pure Mathematics, 12, 178-185. https://doi.org/10.4236/apm.2022.123015
- Doroszlai, Pal, Keller, Horacio (2022) The Exponential Function as Split Infinite Product. Advances in Pure Mathematics, 12, 308-331. https://doi.org/10.4236/apm.2022.124024