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CERTAIN NEW INTEGRAL FORMULAS INVOLVING THE GENERALIZED BESSEL FUNCTIONS

  • Choi, Junesang ;
  • Agarwal, Praveen ;
  • Mathur, Sudha ;
  • Purohit, Sunil Dutt
  • Received : 2013.07.17
  • Published : 2014.07.31

Abstract

A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas involving various Bessel functions have been presented. Very recently, Choi and Agarwal derived two generalized integral formulas associated with the Bessel function $J_{\nu}(z)$ of the first kind, which are expressed in terms of the generalized (Wright) hypergeometric functions. In the present sequel to Choi and Agarwal's work, here, in this paper, we establish two new integral formulas involving the generalized Bessel functions, which are also expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

Keywords

Gamma function;hypergeometric function $_pF_q$;generalized (Wright) hypergeometric functions $_p{\Psi}_q$;Bessel functions;generalized Bessel function of the first kind;Oberhettinger's integral formula

References

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Cited by

  1. SOME INTEGRALS ASSOCIATED WITH MULTIINDEX MITTAG-LEFFLER FUNCTIONS vol.34, pp.3_4, 2016, https://doi.org/10.14317/jami.2016.249
  2. Certain families of integral formulas involving Struve functions vol.37, pp.3, 2017, https://doi.org/10.5269/bspm.v37i3.31890
  3. Inequalities on an extended Bessel function vol.2018, pp.1, 2018, https://doi.org/10.1186/s13660-018-1656-4

Acknowledgement

Supported by : National Research Foundation of Korea