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INTEGRAL REPRESENTATIONS OF THE k-BESSEL'S FUNCTION

Gehlot, Kuldeep Singh;Purohit, Sunil Dutt

  • Received : 2015.04.28
  • Accepted : 2015.12.23
  • Published : 2016.03.25

Abstract

This paper deals with the study of newly defined special function known as k-Bessel's function due to Gehlot [2]. Certain integral representations of k-Bessel's function are investigated. Known integrals of classical Bessel's function are seen to follow as special cases of our main results.

Keywords

k-Gamma function;k-Pochhammer symbols;k-Bessel function

References

  1. R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulgaciones Mathematicas 15(2) (2007), 179-192.
  2. K. S. Gehlot, Differential Equation of k-Bessel's Function and its Properties, Nonl. Anal. Diff. Eq. 2(2) (2014), 61-67.
  3. K. S. Gehlot, Recurrence relations of k-Bessel's function, Thai J. Math. (2015), Accepted.
  4. K. S. Gehlot and S. D. Purohit, Fractional calculus of k-Bessel's function, Acta Univ. Apulensis, Math. Inform. 38 (2014), 273-278.
  5. Earl D. Rainville, Special Functions, The Macmillan Company, New York, 1963.

Cited by

  1. -Bessel Function vol.2018, pp.2314-4785, 2018, https://doi.org/10.1155/2018/5198621
  2. Differential equation and inequalities of the generalized k-Bessel functions vol.2018, pp.1, 2018, https://doi.org/10.1186/s13660-018-1772-1