Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

CERTAIN UNIFIED INTEGRALS INVOLVING PRODUCT OF GENERALIZED k-BESSEL FUNCTION AND GENERAL CLASS OF POLYNOMIALS

  • Menaria, N. (Department of Mathematics, Pacific College of Basic & Applied Sciences) ;
  • Parmar, R.K. (Department of Mathematics, Govt. College of Engineering and Technology) ;
  • Purohit, S.D. (Department of HEAS (Mathematics), Rajasthan Technical University) ;
  • Nisar, K.S. (Department of Mathematics, College of Arts and Science-Wadi Al-dawasir Prince Sattam bin Abdulaziz University)
  • Received : 2016.09.13
  • Accepted : 2017.06.17
  • Published : 2017.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

By means of the Oberhettinger integral, certain generalized integral formulae involving product of generalized k-Bessel function $w^{{\gamma},{\alpha}}_{k,v,b,c}(z)$ and general class of polynomials $S^m_n[x]$ are derived, the results of which are expressed in terms of the generalized Wright hypergeometric functions. Several new results are also obtained from the integrals presented in this paper.

Keywords

References

  1. R.A. Cerutti, On the k-Bessel functions, Int. Math. Forum 7(38)(2012), 1851-1857.
  2. J. Choi, P. Agarwal, S. Mathur and S.D. Purohit, Certain new integral formulas involving the generalized Bessel functions, Bull. Korean Math. Soc. 51(4) (2014), 995-1003. https://doi.org/10.4134/BKMS.2014.51.4.995
  3. R. Diaz and E. Pariguan, On hypergeometric functions and k-Pochhammer symbol, Divulgaciones Mathematicas 15(2) (2007), 179-192.
  4. K. S. Nisar and S.R. Mondal, Certain unified integral formulas involving the generalized modified k-Bessel function of the first kind, arXiv:1601.06487 [math.CA].
  5. K.S. Nisar, R.K. Parmar, and A.H. Abusufian, Certain new unified integrals associated with the generalized k-Bessel function, Far East J. Math. Sci. 7(38) (2016).
  6. N. Menaria, S.D. Purohit and R.K. Parmar, On a new class of integrals involving generalized Mittag-leffer function, Surv. Math. Appl. 11 (2016), 1-9.
  7. 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(3) (2016), 1-5. https://doi.org/10.18576/sjm/030101
  8. F. Oberhettinger, Tables of Mellin Transforms, Springer-Verlag, New York, 1974.
  9. F.W.L. Olver, D.W. Lozier, R.F. Boisvert, C.W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, 2010.
  10. L.G. Romero, G.A. Dorrego and R.A. Cerutti, The k-Bessel function of first kind, Int. Math. Forum 7(38) (2012), 1859-1854.
  11. E.D. Rainville, Special functions, Macmillan, New York, 1960.
  12. H.M. Srivastava, P.W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto, 1985.
  13. H.M. Srivastava, A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), 1-6.
  14. E.M. Wright, The asymptotic expansion of the generalized hypergeometric functions, J. London Math. Soc. 10 (1935), 286-293.
  15. E.M. Wright, The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Roy. Soc., London, A 238 (1940), 423-451. https://doi.org/10.1098/rsta.1940.0002
  16. E.M. Wright, The asymptotic expansion of the generalized hypergeometric function II, Proc. London Math. Soc. 46(2) (1940), 389-408.