On q-Gamma and q-Bessel Functions

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 207)

Abstract

In this paper, we present some characterizations of the q-Gamma and the properties of the q-Bessel functions.

Keywords

q-Gamma function q-Bessel functions 

2000 Mathematics Subject Classification

33B15 

Notes

Acknowledgements

We are grateful to the referee for his constructive remarks improving this paper.

References

  1. 1.
    Askey, R.: The q-gamma and q-beta functions. Appl. Anal. 8(2), 125–141 (1978)Google Scholar
  2. 2.
    Bohr, H., Mollerup, J.: Laerebog i mathematisk Analyse, Vol. III, pp. 149–164. Kopenhage (1922)Google Scholar
  3. 3.
    Brahim, K., Sidomou, Y.: On symmetric q-special functions. Mathematiche LXVIII(Fasc. II), 107–122 (2013)Google Scholar
  4. 4.
    Dattoli, G., Torre, A.: Symmetric q-Bessel functions. Le Mathematiche 51, 153–167 (1996)Google Scholar
  5. 5.
    Laugwitz, D., Rodewald, B.: A simple characterization of the gamma function. Am. Math. Mon. 94, 534–536 (1987)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Elmonser, H., Brahim, K., Fitouhi, A.: Relationship between charaterizations of the q-Gamma functions. J. Inequalities Spec. Funct. 3(4), 50–58 (2012)Google Scholar
  7. 7.
    Fitouhi, A., Hamza, M.M., Bouzeffour, F.: The \(q\)-\(J_\alpha \) Bessel function. J. Approx. Theory 115, 144–166 (2002)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Gasper, G., Rahman, M.: Basic Hypergeometric Series. Encyclopedia of Mathematics and Its Applications, vol. 96, 2nd edn. Cambridge University Press, Cambridge (2004)Google Scholar
  9. 9.
    Ismail, M.E.H.: The zeros of basic Bessel functions. J. Math. Anal. Appl. 86, 1–19 (1982)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Jackson, F.H.: On a \(q\)-definite integrals. Q. J. Pure Appl. Math. 41, 193–203 (1910)MATHGoogle Scholar
  11. 11.
    Kac, V.G., Cheung, P.: Quantum Calculus. Universitext. Springer, New York (2002)CrossRefMATHGoogle Scholar
  12. 12.
    Koelink, H.T., Koornwinder, T.H.: q-special functions, a tutorial, in deformation theory and quantum groups with applications to mathematical physics. Contemp. Math. 134. In: Gerstenhaber M., Stasheff J. (eds.) J. Am. Math. Soc. Providence 141–142 (1992)Google Scholar
  13. 13.
    Koornwinder, T.H.: \(q\)-special functions, a tutorial. Mathematical Preprint Series, Report 94-08, University of Amsterdam, The NetherlandsGoogle Scholar
  14. 14.
    Koornwinder, T.H., Swarttouw, R.F.: On \(q\)-analogue of the Fourier and Hankel transforms. Trans. Am. Math. Soc. 333, 445–461 (1992)Google Scholar
  15. 15.
    Moak, D.S.: The \(q\)-gamma function for \(q\;>\;1\). Aequationes Math. 20, 278–285 (1980)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Remmert, R.: Wielandt’s theorem about the \(\Gamma \) function. Am. Math. Mon. 103, 214–220 (1996)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    De Sole, A., Kac, V.G.: On Integral Representations of \(q\)-Gamma and \(q\)-Beta Function. Department of Mathematics, MIT, CambridgeGoogle Scholar
  18. 18.
    Shen, Y.-Y.: On characterizations of the gamma function. Math. Assoc. Am. 68(4), 301–305 (1995)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculté des Sciences de TunisUniversité de TunisTunisTunisia
  2. 2.Faculté des Sciences de BizerteUniversité de TunisZarzounaTunisia

Personalised recommendations