184
Views
1
CrossRef citations to date
0
Altmetric
Articles

Product formula for the generalized q-Bessel function

&
Pages 1663-1672 | Received 23 Nov 2015, Accepted 03 Sep 2016, Published online: 23 Sep 2016

References

  • A. Baricz and S. Ponnusamy, On Turán type inequalities for modified bessel functions, Proc. Amer. Math. Soc. 141(2) (2013), pp. 523–532. doi: 10.1090/S0002-9939-2012-11325-5.
  • G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Application Vol. 35, Cambridge University Press, Cambridge, 1990.
  • M.E.H. Ismail, The zeros of basic Bessel functions, the functions Jv+ax(x) and associated orthogonal polynomials, J. Math. Anal. Appl. 86 (1982), pp. 1–19.
  • M.E.H. Ismail and R. Zhang, q-Bessel functions and Rogers--Ramanujan type identities (2015). Available at arXiv:1508.06861.
  • F.H. Jackson, The application of basic numbers to Bessel’s and Legendre’s functions, Proc. London Math. Soc. (2) 2 (1903--1904), pp. 192–220.
  • M. Mansour, Generalized q-Bessel function and its properties, Adv. Difference Equ. 2013 (2013), pp. 121.
  • M. Mansour and M.M. Al-Shomarani, New q-analogy of modified Bessel function and the quantum algebra E2(2), J. Comput. Anal. Appl. 15(4) (2013), pp. 655–664.
  • M. Rahman, An addition theorem and some product formulas for q-Bessel functions, Can. J. Math. 40 (1988), pp. 1203–1221.
  • R.F. Swarttouw, An addition theorem and some product formulas for the Hahn-Exton q-Bessel functions, Can. J. Math. 44(4) (1992), pp. 867–879.
  • R.F. Swarttouw, The Hahn-Exton q-Bessel functions, Ph.D. thesis, Delft Technical University, 1992.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.