Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Some Finite Integrals Involving Srivastava's Polynomials and the Aleph Function

  • Bhargava, Alok (Department of Mathematics, Jaipur Engineering College and Research Centre) ;
  • Srivastava, Amber (Department of Mathematics, Swami Keshvanand Institute of Technology, Management and Gramothan) ;
  • Mukherjee, Rohit (Department of Mathematics, Swami Keshvanand Institute of Technology, Management and Gramothan)
  • Received : 2014.08.02
  • Accepted : 2015.11.03
  • Published : 2016.06.23
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Abstract

In this paper, we establish certain integrals involving Srivastava's Polynomials [5] and Aleph Function ([8], [10]). On account of general nature of the functions and polynomials involved in the integrals, our results provide interesting unifications and generalizations of a large number of new and known results, which may find useful applications in the field of science and engineering. To illustrate, we have recorded some special cases of our main results which are also sufficiently general and unified in nature and are of interest in themselves.

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References

  1. P. Agarwal, S. Jain, and M. Chand, Finite integrals involving Jacobi Polynomials and I-Function, Theoretical Mathematics & Applications, 1(1)(2011), 115-123.
  2. F. Brafman, Generating functions of Jacobi and related polynomials, Proc. Amer. Math. Soc., 2(1951), 942-949. https://doi.org/10.1090/S0002-9939-1951-0045875-2
  3. A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vol. 2, Mcgraw Hill, New York, (1953).
  4. I. S. Gradshteyin and I. M. Ryzhik,Table of integrals, Series and Products, 6/e, Academic Press, New Delhi, (2001).
  5. E. D. Rainville, Special Functions, Chelsea Publication Company, Bronx, New York, (1971).
  6. R. K. Saxena, T. K. Pogany, Mathieu type series for the ${\aleph}$- Function occurring in Fokker - Planck equation, Eur. J. Pure Appl. Math., 3(6)(2010), 980-988.
  7. N. Sudland, B. Baumann and T. F. Nonnenmacher, Open Problem: Who knows about the Aleph (${\aleph}$)-Functions?, Fract. Calc. Appl. Anal., 1(4)(1998), 401-402.
  8. H. M. Srivastava, A multilinear generating function for the Konhauser sets of biorthogonal Polynomials suggested by the Laguerre polynomials, Pacific J. Math., 117 (1985), 183-191. https://doi.org/10.2140/pjm.1985.117.183
  9. H. M. Srivastava, K. C. Gupta and S. P. Goyal,The H-function of one and two variables with applications, South Asian publishers, New Delhi and Madras, (1982).
  10. G. Szego, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., Vol. 23, 4th Ed., Amer. Math. Soc., Providence, Rhode Island, (1975).