Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Integral Formulas Involving a Product of Generalized Bessel Functions of the First Kind

  • Choi, Junesang (Department of Mathematics, Dongguk University) ;
  • Kumar, Dinesh (Department of Mathematics and Statistics, Jai Narain Vyas University) ;
  • Purohit, Sunil Dutt (Department of HEAS (Mathematics), Rajasthan Technical University)
  • Received : 2015.02.23
  • Accepted : 2015.11.03
  • Published : 2016.03.23
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Abstract

The main object of this paper is to present two general integral formulas whose integrands are the integrand given in the integral formula (3) and a finite product of the generalized Bessel function of the first kind.

Keywords

References

  1. S. Ali, On some new unified integrals, Adv. Comput. Math. Appl., 1(3)(2012), 151-153.
  2. Y. A. Brychkov, Handbook of Special Functions, Derivatives, Integrals, Series and Other Formulas, CRC Press, Taylor & Francis Group, Boca Raton, London, and New York, 2008.
  3. A. Baricz, Generalized Bessel Functions of the First Kind, Springer-Verlag Berlin, Heidelberg, 2010.
  4. A. Baricz, Geometric properties of generalized Bessel functions of complex order, Mathematica, 48(71)(1)(2006), 13-18.
  5. A. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen, 731(2)(2008), 155-178.
  6. A. Baricz, Jorden-type inequalities for generalized Bessel functions, J. Inequal. Pure and Appl. Math., 9(2)(2008), Art. 39, 6.
  7. J. Choi and P. Agarwal, Certain unified integrals associated with Bessel functions, Bound. Value Probl., 2013(2013):95. https://doi.org/10.1186/1687-2770-2013-95
  8. J. Choi and P. Agarwal, Certain unified integrals involving a product of Bessel functions of the first kind, Honam Math. J., 35(4)(2013), 667-677. https://doi.org/10.5831/HMJ.2013.35.4.667
  9. J. Choi and P. Agarwal, Pathway fractional integral formulas involving Bessel functions of the first kind, Adv. Stud. Contemp. Math., (Kyungshang), (2015), in press.
  10. J. Choi, A. Hasanov, H. M. Srivastava and M. Turaev, Integral representations for Srivastava's triple hypergeometric functions, Taiwanese J. Math., 15(2011), 2751-2762. https://doi.org/10.11650/twjm/1500406495
  11. J. Choi and A. K. Rathie, Evaluation of certain new class of definite integrals, Integral Transforms Spec. Funct., 2015, http://dx.doi.org/10.1080/10652469.2014.1001385
  12. E. Deniz, H. Orhan and H. M. Srivastava, Some suffcient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math., 15(2011), 883-917. https://doi.org/10.11650/twjm/1500406240
  13. C. Fox, The asymptotic expansion of generalized hypergeometric functions, Proc. Lon-don Math. Soc., 27(2)(1928), 389-400.
  14. M. Garg and S. Mittal, On a new unified integral, Proc. Indian Acad. Sci. Math. Sci., 114(2)(2003), 99-101. https://doi.org/10.1007/BF02829845
  15. D. Kumar, S. D. Purohit, A. Secer and A. Atangana, On generalized fractional kinetic equations involving generalized Bessel function of the first kind, Math. Probl. Eng., 2014, Article ID 289387, 1-7.
  16. P. Malik, S.R. Mondal and A. Swaminathan, Fractional Integration of generalized Bessel Function of the First kind, IDETC/CIE, USA, 2011.
  17. F. Oberhettinger, Tables of Mellin Transforms, Springer-Verlag, New York, 1974.
  18. R. K. Saxena, J. Ram and D. Kumar, Generalized fractional integration of the product of Bessel functions of the first kind, Proc. the 9th Annual Conference, SSFA, 9(2010), 15-27.
  19. H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam-London-New York, 2012.
  20. H. M. Srivastava and M. C. Daoust, A note on the convergence of Kampe de Feriet's double hypergeometric series, Math. Nachr., 53(1985), 151-159.
  21. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.
  22. H. M. Srivastava, M. I. Quresh, R. Singh and A. Arora, A family of hypergeometric integrals associated with Ramanujan's integral formula, Adv. Stud. Contemp. Math., 18(2009), 113-125.
  23. H. M. Srivastava, K. A. Selvakumaran and S. D. Purohit, Inclusion properties for certain subclasses of analytic functions defined by using the generalized Bessel functions, Malaya J. Math., 3(2015), 360-367.
  24. H. Tang, H. M. Srivastava, E. Deniz and S.-H. Li, Third-order differential superordination involving the Generalized Bessel functions, Bull. Malays. Math. Sci. Soc., 38(2015), 1669-1688. https://doi.org/10.1007/s40840-014-0108-7
  25. G. N.Watson, A Treatise on The Theory of Bessel Functions, Second Edi., Cambridge University Press, 1996.
  26. E. M. Wright, The asymptotic expansion of the generalized hypergeometric functions, J. London Math. Soc., 10(1935), 286-293.
  27. 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
  28. E. M. Wright, The asymptotic expansion of the generalized hypergeometric function II, Proc. London Math. Soc., 46(2)(1940), 389-408.