New generalizations of the zeta-function and the Tricomi funation

1Virchenko, NO
2Ponomarenko, AM
1NTU of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2National Technical University of Ukraine "Kyiv Polytechnic Institute"
Dopov. Nac. akad. nauk Ukr. 2016, 12:5-11
https://doi.org/10.15407/dopovidi2016.12.005
Section: Mathematics
Language: Ukrainian
Abstract: 

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.

Keywords: confluent hypergeometric function, Tricomi function, zeta-function
References: 
  1. Andrews L.G. Special Function for Engineers and Applied Mathematics, New York: Macmillan Publ. Company, 1985.
  2. Andrews G., Askey R., Roy R. Special Function, New York: Cambridge Univ. Press, 1999. doi:https://doi.org/10.1017/CBO9781107325937
  3. Edwards H.M. Riemann's Zeta Function, New York: Academic Press, 1954.
  4. Ewell J.A. Amer. Math. Monthly, 1990, 97: 219-220. doi: https://doi.org/10.2307/2324688
  5. Titchmarsh E.C. The Theory of Riemann Zeta-Function, London: Oxford Univ. Press, 1951.
  6. Wright E.M. Proc. London Math. Soc, 1940, 46, No 2: 389-408. doi: https://doi.org/10.1112/plms/s2-46.1.389
  7. Virchenko N. Fract. Calculus and App. Anal., 2006, 9, No 2: 101-108.
  8. Virchenko N. The generalized hypergeometric functions, Kiev: NTU of Ukraine "KPI", 2016 (in Ukrainian).
  9. Bateman H., Erdelyi A. Higher Transcendental Functions, New York: McGraw-Hill, 1953, Vol. 1. PMid:13066029 PMCid:PMC1056899
  10. Tricomi F. Funzioni Ipergeometriche Confluenti, Monografie Matematiche, Bd. 1, Roma: Edizioni Cremonese, 1954.