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Certain integrals involving the generalized hypergeometric function and the Laguerre polynomials. (English) Zbl 1351.33008
Summary: The aim of the paper is to establish certain new integrals involving the generalized Gauss hypergeometric function, generalized confluent hypergeometric function, and the Laguerre polynomials. On account of the most general nature of the functions involved therein, our main findings are capable of yielding a large number of new, interesting, and useful integrals, expansion formulas involving the hypergeometric function, and the Laguerre Polynomials as their special cases.

##### MSC:
 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 65A05 Tables in numerical analysis
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##### References:
 [1] Özergin, E.; Özarslan, M. A.; Altin, A., Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math., 235, 4601-4610, (2011), Available online at http://dx.doi.org/10.1016/j.cam.2010.04.019 · Zbl 1218.33002 [2] Özergin, E., Some properties of hypergeometric functions,, (2011), Eastern Mediterranean University, North Cyprus, (Ph.D. thesis) [3] Prabhakar, T. R.; Rekha, S., Some results on the polynomials $$L_n^{\alpha, \beta}(x)$$, Rocky Mountain J. Math., 8, 4, 751-754, (1978), Available online at http://dx.doi.org/10.1216/RMJ-1978-8-4-751 · Zbl 0398.33009 [4] Rainville, E. D., Special functions, (1960), Macmillan New York · Zbl 0050.07401 [5] Konhauser, J. D.E., Biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math., 21, 303-314, (1967) · Zbl 0156.07401 [6] Shukla, A. K.; Prajapati, J. C.; Salehbhai, I. A., On a set of polynomials suggested by the family of konhauser polynomial, Int. J. Math. Anal. (Ruse), 3, 13-16, 637-643, (2009) · Zbl 1198.33006 [7] Oldham, K.; Myland, J.; Spanier, J., An altas of functions—with equator, the atlas function calculator, (2009), Springer New York, Available online at http://dx.doi.org/10.1007/978-0-387-48807-3 [8] Spanier, J.; Oldham, K. B., An altas of functions, (1987), Taylor & Francis/Hemisphere Bristol PA, USA · Zbl 0209.12501 [9] Agarwal, P.; Jain, S.; Chand, M., Certain integrals involving generalized mittage-Leffler function, Proc. Natl. Acad. Sci. India Sect. A Phys. Sci., 85, 3, 359-371, (2015), Available online at http://dx.doi.org/10.1007/s40010-015-0209-1 · Zbl 1325.44003
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