New generalizations of the zeta-function and the Tricomi funation
DOI:
https://doi.org/10.15407/dopovidi2016.12.005Keywords:
confluent hypergeometric function, Tricomi function, zeta-functionAbstract
New generalizations of the zeta-function and the Tricomi function are presented, and their main properties are studied.
These new generalizations are realized with help of the (τ, β)-generalized confluent hypergeometric function.
Downloads
References
Andrews L.G. Special Function for Engineers and Applied Mathematics, New York: Macmillan Publ. Company, 1985.
Andrews G., Askey R., Roy R. Special Function, New York: Cambridge Univ. Press, 1999. doi:https://doi.org/10.1017/CBO9781107325937
Edwards H.M. Riemann's Zeta Function, New York: Academic Press, 1954.
Ewell J.A. Amer. Math. Monthly, 1990, 97: 219-220. doi: https://doi.org/10.2307/2324688
Titchmarsh E.C. The Theory of Riemann Zeta-Function, London: Oxford Univ. Press, 1951.
Wright E.M. Proc. London Math. Soc, 1940, 46, No 2: 389-408. doi: https://doi.org/10.1112/plms/s2-46.1.389
Virchenko N. Fract. Calculus and App. Anal., 2006, 9, No 2: 101-108.
Virchenko N. The generalized hypergeometric functions, Kiev: NTU of Ukraine "KPI", 2016 (in Ukrainian).
Bateman H., Erdelyi A. Higher Transcendental Functions, New York: McGraw-Hill, 1953, Vol. 1. PMid:13066029 PMCid:PMC1056899
Tricomi F. Funzioni Ipergeometriche Confluenti, Monografie Matematiche, Bd. 1, Roma: Edizioni Cremonese, 1954.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
