Jacobi’s generating function for Jacobi polynomials
HTML articles powered by AMS MathViewer
- by Richard Askey PDF
- Proc. Amer. Math. Soc. 71 (1978), 243-246 Request permission
Abstract:
An idea of Hermite is used to give a simple proof of Jacobi’s generating function for Jacobi polynomials.References
- L. Carlitz, The generating function for the Jacobi polynomial, Rend. Sem. Mat. Univ. Padova 38 (1967), 86–88. MR 222357
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391 C. Hermite and T. J. Stieltjes, Correspondance d’Hermite et de Stieltjes, Tome I, edited by B. Baillaud and H. Bourget, Gauthier-Villars, Paris, 1905. —, Correspondance d’Hermite et de Stieltjes, Tome II, edited by B. Baillaud and H. Bourget, Gauthier-Villars, Paris, 1905. C. G. J. Jacobi, Untersuchungen über die Differentialgleichung der hypergeometrischen Reihe, J. Reine Angew. Math. 56 (1859), 149-165, Gesammelte Werke 6, Reimer, Berlin, 1891, reprinted Chelsea, New York, 1969, pp. 184-202. A. M. Legendre, Exercices de calcul intégral sur divers ordres de transcendantes, Vol. 2, Courcier, Paris, 1817.
- Earl D. Rainville, Special functions, The Macmillan Company, New York, 1960. MR 0107725 G. Szegö, Orthogonal polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1975. P. L. Tchebychef, Sur les fonctions analogues à celles de Legendre, Zap. Akad. Nauk 16 (1870), 131-140, Oeuvres, Vol. 2, St. Pétersbourg, 1907, reprinted Chelsea, New York, 1961, pp. 59-68.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 71 (1978), 243-246
- MSC: Primary 33A65
- DOI: https://doi.org/10.1090/S0002-9939-1978-0486693-X
- MathSciNet review: 0486693