Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-15T06:01:55.213Z Has data issue: false hasContentIssue false
  • English
  • Français

Some generating-function equivalences†

Published online by Cambridge University Press:  18 May 2009

H. M. Srivastava
H. M. Srivastava
Affiliation:
Department of Mathematics, University of Victoria, Victoria, British Columbia, Canada, V8W 2Y2
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A generalization is given of a theorem of F. Brafman [1] on the equivalence of generating relations for a certain sequence of functions. The main result, contained in Theorem 2 below, may be applied to several special functions including the classical orthogonal polynomials such as Hermite, Jacobi (and, of course, Legendre and ultraspherical), and Laguerre polynomials.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 1 , March 1975 , pp. 34 - 39
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

REFERENCES

1.Brafman, F., Generating functions and associated Legendre polynomials, Quart. J. Math. (Oxford) (2) 10 (1959), 156–160.Google Scholar
2.Krall, H. L. and Frink, O., A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), 100–115.CrossRefGoogle Scholar
3.Whittaker, E. T. and Watson, G. N., A Course of Modern Analysis,Fourth edition (Cambridge, 1963).Google Scholar