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Some Generating Functions for Laguerre and Hermite Polynomials

Published online by Cambridge University Press:  20 November 2018

Fred Brafman
Fred Brafman*
Affiliation:
Wayne State University and Southern Illinois University
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The Laguerre polynomials Ln(α)(x) have the following hypergeometric and Rodrigues representation (3, pp. 188, 189):

1,

2.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 180 - 187
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Brafman, F., Generating functions of Jacobi and related polynomials, Proc. Amer. Math. Soc. 2 (1951), 942–949.Google Scholar
2. Chaundy, T. W., An extension of the hyper geometric function, Quart. J. Math., 14 (1943), 55–78.Google Scholar
3. Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F., Higher Transcendental Functions, 2 (New York, 1953).Google Scholar
4. Erdélyi, A., Magnus, W., Higher Transcendental Functions, 3 (New York, 1955).Google Scholar
5. Magnus, W. and Oberhettinger, F., Special Functions of Mathematical Physics (New York, 1949).Google Scholar
6. Szegö, G., Orthogonal Polynomials, Colloquium Publications XXIII (Amer. Math. Soc, 1939).Google Scholar
7. Weisner, L., Group-theoretic origin of certain generating functions, Pacific J. Math. 4, supp. 2 (1955), 1033–1039.Google Scholar