본문 바로가기
KERD
논문KCI 등재

An extension of the extended Hurwitz-Lerch Zeta Functions of Two Variables

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

We aim to introduce a further extension of a family of the extended Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate several interesting properties of the extended function such as its integral representations which provide extensions of various earlier corresponding results of two and one variables, its summation formula, its Mellin-Barnes type contour integral representations, its computational representation and fractional derivative formulas. A multi-parameter extension of the extended Hurwitz-Lerch Zeta function of two variables is also introduced. Relevant connections of certain special cases of the main results presented here with some known identities are pointed out.

Abstract

We aim to introduce a further extension of a family of the extended Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate several interesting properties of the extended function such as its integral representations which provide extensions of various earlier corresponding results of two and one variables, its summation formula, its Mellin-Barnes type contour integral representations, its computational representation and fractional derivative formulas. A multi-parameter extension of the extended Hurwitz-Lerch Zeta function of two variables is also introduced. Relevant connections of certain special cases of the main results presented here with some known identities are pointed out.

참고문헌 (25)

  1. E. W. Barnes, "The asymptotic expansion of integral functions defined by Taylor series", Philos. Trans. Roy. Soc. London Ser. A, 206, pp.249~297 (1906)
  2. M. A. Chaudhry, "On a Class of Incomplete Gamma Functions with Applications" (2001), Chapman and Hall, (CRC Press Company)
  3. J. Choi, "A generalization of the Hurwitz-Lerch Zeta function", Integral Transforms Spec. Funct, 19(1-2), pp.65~79 (2008)
  4. O. Daman, "A further generalization of the Hurwitz Zeta function", Math. Sci. Res. J, 16(10), pp.251~259 (2012)
  5. A. Erdelyi, "Higher Transcendental Functions. Vol. I" (1953), McGraw-Hill Book Company
  6. M. Garg, "A further study of general Hurwitz-Lerch zeta func-tion", Algebras Groups Geom, 25, pp.311~319 (2008)
  7. S. P. Goyal, "On the generalized Zeta function and the generalized Lambert function", Ganita Sandesh, 11(2), pp.99~108 (1997)
  8. N. T. Hai, "The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory" (1992), World Scientific
  9. D. Jankov, "An extended general Hurwitz-Lerch Zeta function as a Mathieu (a,λ)-series", Appl. Math. Lett, 24(8), pp.1473~1476 (2011)
  10. A. A. Kilbas, "Theory and Applications of Fractional Differential Equations" (2006), Elsevier (North-Holland) Science Publishers
  11. S. D. Lin, "Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations", Appl. Math. Comput, 154(3), pp.725~733 (2004)
  12. A. M. Mathai, "Generalized Hypergeometric Functions with Applica-tions in Statistics and Physical Sciences" (1973), Springer-Verlag
  13. A. M. Mathai, "The H-function with Applications in Statistics and Other Disciplines" (1978), Wiley Eastern Ltd. New Delhi and John Wiley and Sons, Inc
  14. A. M. Mathai, "The H-Functions: Theory and Appli-cations" (2010), Springer
  15. R. B. Paris, "Asymptotic and Mellin-Barnes Integrals" (2001), Cambridge Uni-versity Press
  16. M. A. Pathan, "On generalization of Hurwitz zeta function", ~
  17. S. G. Samko, "Fractional Integrals and Derivatives:Theory and Applications, Translated from the Russian: Integrals and Derivatives of Fractional Order and Some of Their Applications ("Nauka i Tekhnika", Minsk, 1987)", Gordon and Breach Science Publishers, ~ (1993)
  18. H. M. Srivastava, "A new family of the λ-generalized Hurwitz-Lerch Zeta functions with applications", Appl. Math. Inf. Sci, 8(4), pp.1485~1500 (2014)
  19. H. M. Srivastava, "Series Associated with the Zeta and Related Functions" (2001), Kluwer, Acedemic Publishers
  20. H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier Sci-ence, Publishers
  21. H. M. Srivastava, "Two-sided inequalities for the extended Hurwitz-Lerch Zeta function", Comput. Math. Appl, 62(1), pp.516~522 (2011)
  22. H. M. Srivastava, "Multiple Gaussian Hypergeometric Series" (1985), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons
  23. H. M. Srivastava, "New results involving a class of generalized Hurwitz-Lerch Zeta functions and their applications", Turkish J. Anal. Number Theory, 1(1), pp.26~35 (2013)
  24. H. M. Srivastava, "A Treatise on Generating Functions" (1984), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons
  25. H. M. Srivastava, "Integral and computa-tional representations of the extended Hurwitz-Lerch Zeta function", Integral Transforms Spec. Funct, 22(7), pp.487~506 (2011)

관련 논문AI추천

이 간행물의 다른 논문 (24건)