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An equivalence theorem on generating functions. (English) Zbl 0311.33014


MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33C55 Spherical harmonics
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
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References:

[1] F. Brafman, Generating functions and associated Legendre polynomials, Quart. J. Math. Oxford Ser. (2) 10 (1959), 156 – 160. · Zbl 0087.28203
[2] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions. Vol. II, McGraw-Hill, New York, 1953. MR 15, 419. · Zbl 0051.30303
[3] H. L. Krall and Orrin Frink, A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), 100 – 115. · Zbl 0031.29701
[4] G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1939. MR 1, 14. · JFM 65.0278.03
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