A short proof of a generating function for Jacobi polynomials
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- by Dennis Stanton PDF
- Proc. Amer. Math. Soc. 80 (1980), 398-400 Request permission
Abstract:
A short proof is given for Bailey’s bilinear generating function for Jacobi polynomials. It depends only upon the orthogonality relation for Jacobi polynomials and a quadratic transformation for a hypergeometric series. A q-analog is also stated.References
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- Richard Askey, Orthogonal polynomials and special functions, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1975. MR 0481145
- Richard Askey, Jacobi’s generating function for Jacobi polynomials, Proc. Amer. Math. Soc. 71 (1978), no. 2, 243–246. MR 486693, DOI 10.1090/S0002-9939-1978-0486693-X W. Bailey, The generating function of Jacobi polynomials, J. London Math. Soc. 13 (1938), 8-12. —, Generalized hypergeometric series, Cambridge Univ. Press, Cambridge, 1935.
- L. Carlitz, Some formulas of F. H. Jackson, Monatsh. Math. 73 (1969), 193–198. MR 248035, DOI 10.1007/BF01300534
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 398-400
- MSC: Primary 33A65; Secondary 42C10
- DOI: https://doi.org/10.1090/S0002-9939-1980-0580992-8
- MathSciNet review: 580992