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http://dx.doi.org/10.5666/KMJ.2019.59.4.725

Integral Formulas Involving Product of Srivastava's Polynomials and Galué type Struve Functions  

Suthar, Daya Lal (Department of Mathematics, Wollo University)
Andualem, Mitku (Department of Mathematics, Wollo University)
Publication Information
Kyungpook Mathematical Journal / v.59, no.4, 2019 , pp. 725-734 More about this Journal
Abstract
The aim of this paper is to establish two general finite integral formulas involving the product of Galué type Struve functions and Srivastava's polynomials. The results are given in terms of generalized (Wright's) hypergeometric functions. These results are obtained with the help of finite integrals due to Oberhettinger and Lavoie-Trottier. Some interesting special cases of the main results are also considered. The results presented here are of general character and easily reducible to new and known integral formulae.
Keywords
$Galu{\acute{e}}$ type Struve function; gamma function; generalized Wright function; Oberhettinger integral formula; Lavoie-Trottier integral formula;
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  • Reference
1 R. P. Singh, Infinite integral involving generalized Struve function, Math. Ed. (Siwan), 23(1989), 30-36.
2 H. M. Srivastava, A contour integral involving Fox's H-function, Indian J. Math., 14(1972), 1-6.
3 H. M. Srivastava and J. Choi, Zeta and q-Zeta functions and associated series and integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
4 H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.
5 D.L. Suthar and H. Amsalu, Certain integrals associated with the generalized Bessel-Maitland function, Appl. Appl. Math., 12(2)(2017), 1002-1016.
6 D. L. Suthar, S. D. Purohit and R. K. Parmar, Generalized fractional calculus of the multiindex Bessel function, Math. Nat. Sci., 1(2017), 26-32.   DOI
7 D. L. Suthar, G. V. Reddy and T. Tsagye, Unified integrals formulas involving product of Srivastava's polynomials and generalized Bessel-Maitland function, Int. J. Sci. Res., 6(2)(2017), 708-710.
8 E.M. Wright, The asymptotic expansion of the generalized hypergeometric functions, J. London Math. Soc., 10(1935), 286-293.   DOI
9 A: Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen, 73(1-2)(2008), 155-178.
10 A: Baricz, Generalized Bessel functions of the first kind, Lect. Notes Math. 1994, Springer-Verlag, Berlin, 2010.
11 K. N. Bhowmick, Some relations between a generalized Struve's function and hyper-geometric functions, Vijnana Parishad Anusandhan Patrika, 5(1962), 93-99.
12 K. N. Bhowmick, A generalized Struve function and its recurrence formula, Vijnana Parishad Anusandhan Patrika, 6(1963), 1-11.
13 K. S. Nisar, D. L. Suthar, S. D. Purohit and M. Aldhaifallah, Some unified integrals associated with the generalized Struve function, Proc. Jangjeon Math. Soc., 20(2)(2017), 261-267.
14 B. N. Kanth, Integrals involving generalised Struve's function, Nepali Math. Sci. Rep., 6(1981), 61-64.
15 J. L. Lavoie, and G. Trottier, On the sum of certain Appell series, Ganita, 20(1969), 43-66.
16 N. Menaria, D. Baleanu and S. D. Purohit, Integral formulas involving product of general class of polynomials and generalized Bessel function, Sohag J. Math., 3(2)(2016), 77-81.   DOI
17 K. S. Nisar, P. Agarwal and S. R. Mondal, On fractional integration of generalized Struve functions of first kind, Adv. Stud. Contemp. Math., 26(1)(2016), 63-70.
18 K. S. Nisar, D. Baleanu and M. M. A. Qurashi, Fractional calculus and application of generalized Struve function, SpringerPlus; Heidelberg 5(1)(2016), 1-13, DOI 10.1186/s40064-016-2560-3.
19 F. Oberhettinger, Tables of Mellin transforms, Springer-Verlag, New York, 1974.
20 H. Orhan and N. Yagmur, Starlikeness and convexity of generalized Struve functions, Abstr. Appl, Anal., (2013), Art. ID 954513, 6 pp.
21 C. Fox, The asymptotic expansion of generalized hypergeometric functions, Proc. London Math. Soc. (2), 27(5)(1928), 389-400.   DOI
22 H. Orhan and N. Yagmur, Geometric properties of generalized Struve functions, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 63(2017), 229--244.
23 S. D. Purohit, D. L. Suthar and S. L. Kalla, Marichev-Saigo-Maeda fractional integration operators of the Bessel functions, Matematiche (Catania), 67(1)(2012), 21-32.
24 R. P. Singh, Some integral representation of generalized Struve's function, Math. Ed. (Siwan), 22(1988), 91-94.