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http://dx.doi.org/10.4134/CKMS.c200195

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

Jangid, Nirmal Kumar (Department of Mathematics & Statistics Manipal University Jaipur)
Joshi, Sunil (Department of Mathematics & Statistics Manipal University Jaipur)
Purohit, Sunil Dutt (Department of HEAS (Mathematics) Rajasthan Technical University)
Suthar, Daya Lal (Department of Mathematics Wollo University)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.2, 2021 , pp. 267-276 More about this Journal
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
Hurwitz-Lerch zeta function; extended Wright-Bessel (Bessel-Maitland) function; pathway fractional integral operator;
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1 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
2 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.
3 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   DOI
4 T. Pohlen, The Hadamard product and universal power series, Ph.D. Thesis, Universitt Trier, Trier, Germany, 2009.
5 G. Rahman, K. S. Nisar and M. Arshad, A new extension of Hurwitz-Lerch zeta function, arXiv:1802.07823v1[math.CA], 2018.
6 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   DOI
7 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.   DOI
8 E. M. Wright, The asymptotic expansion of the generalized hypergeometric functions, J. London Math. Soc. 10 (1935), 286-293.   DOI
9 P. Agarwal and S. D. Purohit, The unified pathway fractional integral formulae, J. Fract. Calc. Appl. 4 (2013), no. 1, 105-112.
10 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   DOI
11 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).
12 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   DOI
13 A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Higher Transcendental Functions. Vol.1, McGraw-Hill, New York, Toronto, London, 1955.
14 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   DOI
15 A. M. Mathai and H. J. Haubold, On generalized distributions and pathways, Phys. Lett. A 372 (2008), 2109-2113.   DOI
16 S. S. Nair, Pathway fractional integration operator, Fract. Calc. Appl. Anal. 12 (2009), no. 3, 237-252.