Skip to main content
SpringerLink
Log in

Generating Relations of the Hypergeometric Functions by the Lie Group-Theoretic Method

  • Published:
Mathematical Physics, Analysis and Geometry Aims and scope Submit manuscript

Abstract

In this paper, the generating relations for a set of hypergeometric functions ψα,β,γ,m (x) are obtained by using the representation of the Lie group SL(2,C) giving a suitable interpretation to the index m in order to derive the elements of Lie algebra. The principle interest in our results lies in the fact that a number of special cases would inevitably yield too many new and known results of the theory of special functions, namely the Laguerre, even and odd generalized Hermite, Meixner, Gottlieb, and Krawtchouk polynomials.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Rainville, E. D.: Special Functions, Macmillan, New York, 1960.

    Google Scholar 

  2. Szegö, G.: Orthogonal Polynomials, 4th edn, Amer. Math. Soc. Colloq. Publ. 23, Amer. Math. Soc., Providence, Rhode Island, 1975.

    Google Scholar 

  3. Srivastava, H. M. and Manocha, H. L.: A Treatise on Generating Functions, Ellis Horwood, England, 1984.

    Google Scholar 

  4. Chihara, T. S.: An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.

    Google Scholar 

  5. Miller, W.: Lie Theory and Special Functions, Academic Press, New York, 1968.

    Google Scholar 

  6. Khanna, I. K. and Srinivasa Bhagavan, V.: Weisner's method to obtain generating relations for the generalized polynomial set, J. Phys. AMath. Gen. 32 (1999), 1-10.

    Google Scholar 

  7. Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.: Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953.

    Google Scholar 

  8. Cohn, P. M.: Lie Groups, Cambridge Univ. Press, Cambridge, 1961.

    Google Scholar 

  9. Vilenkin, N. Ja. and Klimyk, A. U.: Representation of Lie Groups and Special Functions, Vols. 1 and 2, Kluwer Acad. Publ., Dordrecht, 1991, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi, 221005, India

    I. K. Khanna, V. Srinivasa Bhagavan & M. N. Singh

Authors
  1. I. K. Khanna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Srinivasa Bhagavan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. N. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khanna, I.K., Bhagavan, V.S. & Singh, M.N. Generating Relations of the Hypergeometric Functions by the Lie Group-Theoretic Method. Mathematical Physics, Analysis and Geometry 3, 287–303 (2000). https://doi.org/10.1023/A:1011409221481

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011409221481

Search

Navigation