On Extended Hurwitz-Lerch Zeta Function
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This paper investigates an extended form Hurwitz-Lerch zeta function, as well as related integral images, ordinary and fractional derivatives, and series expan sions, using the term extended beta function. In addition, we establish a connection between the extended Hurwitz-Lerch zeta function and the Laguerre polynomials. Fur thermore, we present a probability distribution application of the extended Hurwitz-Lerch zeta functionζδ,µν,λ. Several (known and new) results are shown to follow as special cases of our findings.
Abstract
This paper investigates an extended form Hurwitz-Lerch zeta function, as well as related integral images, ordinary and fractional derivatives, and series expan sions, using the term extended beta function. In addition, we establish a connection between the extended Hurwitz-Lerch zeta function and the Laguerre polynomials. Fur thermore, we present a probability distribution application of the extended Hurwitz-Lerch zeta functionζδ,µν,λ. Several (known and new) results are shown to follow as special cases of our findings.
참고문헌 (30)
- E. W. Barnes, "The theory of the double gamma function", Philos. Trans. Roy. Soc. (A), 196, pp.265~387 (1901)
- E. W. Barnes, "On the theory of the double gamma function", Trans. Cambridge Phil. Soc, 19, pp.374~425 (1904)
- C. Berge, "Principles of combinatorics" (1971), Academic Press
- Maged G. Bin-Saad, "Sums and partial sums of double power series associated with the generalized zeta function and their N-fractional calculus", Math. J. Okayama University, 49, pp.37~52 (2007)
- Maged G. Bin-Saad, "Hypergeometric series associated with the Hurwitz-Lerch zeta function", Acta Math. Univ. Comenian, 78, pp.269~286 (2009)
- M. A. Chaudhry, "Generalized incomplete gamma function with applications", J. Comput. Appl. Math, 55, pp.99~124 (1994)
- M. A. Chaudhry, "Extension of Euler’s beta function", J. Comput. Appl. Math, 78, pp.19~32 (1997)
- M. A. Chaudhry, "Extended hypergeometric and confluent hypergeometric functions", Appl. Math. Comput, 159, pp.589~602 (2004)
- M. A. Chaudhry, "On a class of incomplete gamma functions with applications" (2002), CRC Press (Chapman and Hall)
- A. Erd´elyi, "Higher Transcendental Functions, Vol. I" (1953), McGraw-Hill
- O. Espinosa, "On some integrals involving the Hurwitz zeta function:Part 2", The Ramanujan J, 6, pp.159~188 (2002)
- O. Espinosa, "A generalized poly gamma function", Integral Transforms Spec. Funct, 15(2), pp.101~115 (2004)
- H. Exton, "Multiple hypergeometric functions and applications" (1976), Halsted Press
- M. Garg, "A further study of general Hurwitz-Lerch zeta function", Algebras Groups Geom, 25, pp.311~319 (2008)
- S. Goyal, "On the generalized Riemann zeta function and the generalized Lambert transform", Ganita Sandesh, 11, pp.99~108 (1997)
- S. Kanemitsu, "On the Hurwitz-Lerch zeta function", Aequationes Math, 59, pp.1~19 (2000)
- M. Katsurada, "An application of Mellin-Barnes type integrals to the mean square of Lerch zeta-function", Collect. Math, 48, pp.137~153 (1997)
- D. Klusch, "On the Taylor expansion of Lerch zeta-function", J. Math. Anal. Appl, 170, pp.513~523 (1992)
- V. Kumar, "On the generalized hurwitz-lerch zeta function and generalized lambert transform", J. Class. Anal, 17(1), pp.55~67 (2021)
- C. A. Larry, "Special functions of mathematics for engineers" (1998), SPIE Press and Oxford University Press
- K. Matsumoto, "Number theory for the millennium, II", pp.417~440 (2000)
- K. S. Miller, "An introduction to the fractional calculus and fractional differential equations" (1993), New York
- M. A. Ozaraslan, "Some remarks on extended hypergeometric, extended confluent hypergeometric and extended Appell’s functions", J. Comput. Anal. Appl, 14(6), pp.1148~1153 (2012)
- A. P. Prudnikov, "Integrals and Series, Volume 3" (1990), Gordon and Breach Science Publishers
- R. K. Parmar, "On a certain extension of the Hurwitz-Lerch zeta functionm", An. Univ. Vest Timis. Ser. Mat. -Inform, 52(2), pp.157~170 (2014)
- S. Ramanujan, "A series for Euler’s constant γ", Messenger Math, 46, pp.73~80 (1917)
- R. K. Raina, "Certain results involving a class of functions associated with the Hurwitz zeta function", Acta. Math. Univ. Comenianae, 1, pp.89~100 (2004)
- L. J. Slater, "Confluent hypergeometric functions" (1960), Cambridge Univ., Press
- H. M. Srivastava, "Multiple Gaussian Hypergeometric Series" (1985), Halsted Press
- E. T. Whittaker, "A Course of Modern Analysis" (1927), Cambridge Univ. Press
