DOI QR코드

DOI QR Code

THE COMPOSITION OF HURWITZ-LERCH ZETA FUNCTION WITH PATHWAY INTEGRAL OPERATOR

  • Received : 2020.06.05
  • Accepted : 2020.11.23
  • Published : 2021.04.30

Abstract

The aim of the present investigation is to establish the composition formulas for the pathway fractional integral operator connected with Hurwitz-Lerch zeta function and extended Wright-Bessel function. Some interesting special cases have also been discussed.

Keywords

Acknowledgement

The authors are thankful to the referee for his valuable suggestion in the improvement of the present work.

References

  1. P. Agarwal and S. D. Purohit, The unified pathway fractional integral formulae, J. Fract. Calc. Appl. 4 (2013), no. 1, 105-112.
  2. M. Arshad, S. Mubeen, K. S. Nisar, and G. Rahman, Extended Wright-Bessel function and its properties, Commun. Korean Math. Soc. 33 (2018), no. 1, 143-155. https://doi.org/10.4134/CKMS.c170039
  3. M. A. Chaudhry, A. Qadir, M. Rafique, and S. M. Zubair, Extension of Euler's beta function, J. Comput. Appl. Math. 78 (1997), no. 1, 19-32. https://doi.org/10.1016/S0377-0427(96)00102-1
  4. J. Choi and P. Agarwal, Certain inequalities involving pathway fractional integral operators, Kyungpook Math. J. 56 (2016), no. 4, 1161-1168. https://doi.org/10.5666/KMJ.2016.56.4.1161
  5. A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Higher Transcendental Functions. Vol.1, McGraw-Hill, New York, Toronto, London, 1955.
  6. M. Garg, K. Jain, and S. L. Kalla, A further study of general Hurwitz-Lerch zeta function, Algebras Groups Geom. 25 (2008), no. 3, 311-319.
  7. S. P. Goyal and R. K. Laddha, On the generalized Riemann zeta functions and the generalized Lambert transform, Ganita Sandesh 11 (1997), no. 2, 99-108 (1998).
  8. A. M. Mathai, A pathway to matrix-variate gamma and normal densities, Linear Algebra Appl. 396 (2005), 317-328. https://doi.org/10.1016/j.laa.2004.09.022
  9. A. M. Mathai and H. J. Haubold, On generalized distributions and pathways, Phys. Lett. A 372 (2008), 2109-2113. https://doi.org/10.1016/j.physleta.2007.10.084
  10. S. S. Nair, Pathway fractional integration operator, Fract. Calc. Appl. Anal. 12 (2009), no. 3, 237-252.
  11. R. K. Parmar and R. K. Raina, On a certain extension of the Hurwitz-Lerch zeta function, An. Univ. Vest Timis. Ser. Mat.-Inform. 52 (2014), no. 2, 157-170. https://doi.org/10.2478/awutm-2014-0017
  12. T. Pohlen, The Hadamard product and universal power series, Ph.D. Thesis, Universitt Trier, Trier, Germany, 2009.
  13. G. Rahman, K. S. Nisar and M. Arshad, A new extension of Hurwitz-Lerch zeta function, arXiv:1802.07823v1[math.CA], 2018.
  14. R. K. Saxena, J. Daiya, and A. Singh, Integral transforms of the k-generalized MittagLeffler function Eγ,τκ,α,β(z), Matematiche (Catania) 69 (2014), no. 2, 7-16. https://doi.org/10.4418/2014.69.2.2
  15. M. Shadab, S. Jabee, and J. Choi, An extension of beta function and its application, Far East J. Math, Sci. 103 (2018), no. 1, 235-251. https://doi.org/10.17654/ms103010235
  16. E. M. Wright, The asymptotic expansion of the generalized hypergeometric functions, J. London Math. Soc. 10 (1935), 286-293. https://doi.org/10.1112/jlms/s1-10.40.286