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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
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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