Beta type integral operator associated with Wright generalized Bessel function
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Abstract
The object of the present paper is to establish integral involving Wrightgeneralized Bessel function (or generalized Bessel-Maitland function) J^{\mu,\gamma}_{\nu, q}defined by Singh et al. [21], which are expressed in the terms of generalized (Wright)hypergeometric functions. Some interesting special cases involving Bessel functions,generalized Bessel functions, generalized Mittag-Leffler functions are deduced.
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Nisar, K., & Khan, W.
(2018).
Beta type integral operator associated with Wright generalized Bessel function.
Acta Mathematica Universitatis Comenianae, 87(1), 117-125.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/621/539
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References
1. Ali, S, On an interesting integral involving Gauss's hypergeometric function, Adv. Comput. Sci. Appl., Vol. 14(2012), 244-246.
2. Abouzaid, M.S, Abusuan, A.H and Nisar K S, Some unified integrals associated with generalized Bessel-Maitland function , Int. Bull. Math. Res., 3(1)(2016), 2394-7802.
3. Choi, J, Agarwal, P, Mathur, S and Purohit, S.D, Certain new integral formulas involving the generalized Bessel functions, Bull. Korean Math. Soc., 514(2014), 995-1003.
4. Choi, J, Agarwal, P, Certain unified integrals involving a product of Bessel functions of first kind, Honam Mathematical J., 354(2013), 667-677.
5. Choi, J, Agarwal, P, Certain unified integrals associated with Bessel functions, Boundary Value Problem, 201395( 2013).
6. Fox, C, The asymptotic expansion of generalized hypergeometric functions, Proc. Lond. Math. Soc. 27(1928), 389-400.
7. Ghayasuddin, M, Khan, W.A, Mishra, L.N, On hankel type integral transform associated Whittaker and hypergeometric functions, Thai J. Math., accepted (2017).
8. Ghayasuddin, M, Khan, W.A, Araci, S, A new extension of Bessel-Maitland function and its properties, Submitted, (2017).
9. Jain, S, Agarwal, P, A new class of integral relation involving general class of polynomials and I-functions, Walailak J. Sci. Tech.,( 2015).
10. Khan, N.U and Kashmin, T, Some integrals for the generalized Bessel-Maitland functions, Elec. J. Math. Anal. Appl., 4(2)(2016), 139-149.
11. Khan, N.U, Ghayasuddin, M, Talha, M, On certain integral formulas involving the product of Bessel function and Jacobi polynomial, Tamkang J. Math., 47(3)(2016), 339-349.
12. Khan, N.U, Khan, S.W, Ghayasuddin, M, Some new results associated with Bessel-Struve kernel function, Acta Universitatis Apulensis, 48(2016), 89-101
.
13. MacRobert, T.M, Beta functions formulae and integrals involving -function, Math. Annnalen, 142(1961), 450-452.
14. Marichev, O.I, Handbook of integral transform and higher transcendental functions, Ellis Harwood, Chichester (John Wiley and Sons), New York, (1983).
15. Mittag-Leffler, G.M, Sur la nouvelle fonction E(x), CR Acad. Sci., Paris, 137(1903), 554-558.
16. Prabhakar, T.R, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J. 19(1971), 75.
17. Rainville, E.D, Special functions, The Macmillan Company, New York, 1960.
18. Rathie, A.K, A new generalization of generalized hypergeometric function, Le Matematiche, LII(II)(1997), 297-310.
19. Shukla, A.K, Prajapati, J.C, On a generalized Mittag-Leffler function and its properties, J. Math. Anal. Appl., 336(2007), 797-811.
20. Srivastava, H.M and Karlsson, P.W, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester, U.K.), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, (1985).
21. Singh, M, Khan, M.A, Khan, A.H, On some properties of a generalization of Bessel-Maitland function, Int. J. Math. Trends and Tech., 14(1)(2014), 46-54.
22. Wiman, A, Uber den fundamental satz in der theorie der funcktionen, E(x), Acta Math., 29(1905), 191-201.
23. Wright, E.M, The asymptotic expansion of the generalized hypergeometric functions, J. Lond. Math. Soc., 10(1935), 286-293.
24. Wright, E.M, The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. R. Soc. Lond. A, 238(1940), 423-451.
25. Wright, E M, The asymptotic expansion of the generalized hypergeometric function II, Proc. Lond. Math. Soc., 46(1940), 389-408.
2. Abouzaid, M.S, Abusuan, A.H and Nisar K S, Some unified integrals associated with generalized Bessel-Maitland function , Int. Bull. Math. Res., 3(1)(2016), 2394-7802.
3. Choi, J, Agarwal, P, Mathur, S and Purohit, S.D, Certain new integral formulas involving the generalized Bessel functions, Bull. Korean Math. Soc., 514(2014), 995-1003.
4. Choi, J, Agarwal, P, Certain unified integrals involving a product of Bessel functions of first kind, Honam Mathematical J., 354(2013), 667-677.
5. Choi, J, Agarwal, P, Certain unified integrals associated with Bessel functions, Boundary Value Problem, 201395( 2013).
6. Fox, C, The asymptotic expansion of generalized hypergeometric functions, Proc. Lond. Math. Soc. 27(1928), 389-400.
7. Ghayasuddin, M, Khan, W.A, Mishra, L.N, On hankel type integral transform associated Whittaker and hypergeometric functions, Thai J. Math., accepted (2017).
8. Ghayasuddin, M, Khan, W.A, Araci, S, A new extension of Bessel-Maitland function and its properties, Submitted, (2017).
9. Jain, S, Agarwal, P, A new class of integral relation involving general class of polynomials and I-functions, Walailak J. Sci. Tech.,( 2015).
10. Khan, N.U and Kashmin, T, Some integrals for the generalized Bessel-Maitland functions, Elec. J. Math. Anal. Appl., 4(2)(2016), 139-149.
11. Khan, N.U, Ghayasuddin, M, Talha, M, On certain integral formulas involving the product of Bessel function and Jacobi polynomial, Tamkang J. Math., 47(3)(2016), 339-349.
12. Khan, N.U, Khan, S.W, Ghayasuddin, M, Some new results associated with Bessel-Struve kernel function, Acta Universitatis Apulensis, 48(2016), 89-101
.
13. MacRobert, T.M, Beta functions formulae and integrals involving -function, Math. Annnalen, 142(1961), 450-452.
14. Marichev, O.I, Handbook of integral transform and higher transcendental functions, Ellis Harwood, Chichester (John Wiley and Sons), New York, (1983).
15. Mittag-Leffler, G.M, Sur la nouvelle fonction E(x), CR Acad. Sci., Paris, 137(1903), 554-558.
16. Prabhakar, T.R, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J. 19(1971), 75.
17. Rainville, E.D, Special functions, The Macmillan Company, New York, 1960.
18. Rathie, A.K, A new generalization of generalized hypergeometric function, Le Matematiche, LII(II)(1997), 297-310.
19. Shukla, A.K, Prajapati, J.C, On a generalized Mittag-Leffler function and its properties, J. Math. Anal. Appl., 336(2007), 797-811.
20. Srivastava, H.M and Karlsson, P.W, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester, U.K.), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, (1985).
21. Singh, M, Khan, M.A, Khan, A.H, On some properties of a generalization of Bessel-Maitland function, Int. J. Math. Trends and Tech., 14(1)(2014), 46-54.
22. Wiman, A, Uber den fundamental satz in der theorie der funcktionen, E(x), Acta Math., 29(1905), 191-201.
23. Wright, E.M, The asymptotic expansion of the generalized hypergeometric functions, J. Lond. Math. Soc., 10(1935), 286-293.
24. Wright, E.M, The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. R. Soc. Lond. A, 238(1940), 423-451.
25. Wright, E M, The asymptotic expansion of the generalized hypergeometric function II, Proc. Lond. Math. Soc., 46(1940), 389-408.