Gaussian Integrals and the Rogers-Ramanujan Identities

  • D. Stanton

Abstract

It is well known that the Fourier transform of a Gaussian is a Gaussian. In this paper it is shown that a q-analogue of this integral gives the Rogers-Ramanujan identities.

Keywords

Rogers-Ramanujan Hermite polynomials 

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References

  1. [1]
    G. Andrews, The Theory of Partitions, Addison-Wesley, Reading, 1976.MATHGoogle Scholar
  2. [2]
    K. Garrett, M.E.H. Ismail, and D. Stanton, Variants of the Rogers-Ramanujan identities, Adv. Appl. Math. 23 (1999), 274–299.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.MATHGoogle Scholar
  4. [4]
    M.E.H. Ismail and D. Stanton, Multibasic integrals and identities of RogersRamanujan type, in preparation.Google Scholar
  5. [5]
    L.J. Rogers, Second memoir on the expansion of certain infinite products, Proc. Lon. Math. Soc. 25 (1894), 318–343.CrossRefGoogle Scholar
  6. [6]
    L. Slater, Further identities of the Rogers-Ramanujan type, Proc. Lon. Math. Soc. (2) 54, 1952, 147–167.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • D. Stanton
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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