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Generating functions for Jacobi and related polynomials


Author: I. A. Khan
Journal: Proc. Amer. Math. Soc. 32 (1972), 179-186
MSC: Primary 33A65
DOI: https://doi.org/10.1090/S0002-9939-1972-0348161-X
MathSciNet review: 0348161
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Abstract | References | Similar Articles | Additional Information

Abstract: In the present paper, we have established the following relation involving Kampe de Feriet's double hypergeometric function of superior order

$\displaystyle F\left[ {\begin{array}{*{20}{c}} p \\ 1 \\ q \\ 0 \\ \end{array} ... ...n{array}{*{20}{c}} { - n,b;} \\ {1 + b' - n;} \\ \end{array} x} \right]{y^n},} $

which yields a number of interesting generating formulae for Jacobi and related polynomials.

A large number of special cases have been also discussed.


References [Enhancements On Off] (What's this?)

  • [1] P. Appell and J. Kampe de Feriet, Fonctions hypergeometriques et hyperspheriques, Gauthier-Villars, Paris, 1926.
  • [2] F. Brafman, Generating functions of Jacobi and related polynomials, Proc. Amer. Math. Soc. 2 (1951), 942-949. MR 13, 649. MR 0045875 (13:649i)
  • [3] L. Carlitz, A bilinear generating function for the Jacobi polynomials, Boll. Un. Mat. Ital. (3) 18 (1963), 87-89. MR 27 #3841. MR 0153880 (27:3841)
  • [4] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions. Vol. I, McGraw-Hill, New York, 1953. MR 15, 419.
  • [5] -, Higher transcendental functions. Vol. II, McGraw-Hill, New York, 1953. MR 15, 419.
  • [6] E. Feldheim, Relations entre les polynomes de Jacobi, Laguerre et Hermite, Acta Math. 75 (1942), 117-138. MR 7, 65. MR 0012724 (7:65b)
  • [7] R. N. Jain, A generating function for Gegenbauer polynomials, Ricerca (Napoli) (2) 20 (1969), gennaio-aprile, 28-30. MR 40 #4501. MR 0251270 (40:4501)
  • [8] -, Some generating functions for Gegenbauer polynomials, J. Reine Angew. Math. 235 (1969), 108-114. MR 39 #3059. MR 0241720 (39:3059)
  • [9] H. L. Manocha, Bilinear and trilinear generating functions for Jacobi polynomials, Proc. Cambridge Philos. Soc. 64, (1968), 687-690. MR 37 #1663. MR 0226073 (37:1663)
  • [10] -, Some bilinear generating functions for Jacobi poylnomials, Proc. Cambridge Philos. Soc. 63 (1967), 457-459. MR 35 #1847. MR 0210962 (35:1847)
  • [11] E. D. Rainville, Special functions, Macmillan, New York, 1960. MR 21 #6447. MR 0107725 (21:6447)
  • [12] G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R.I., 1939.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0348161-X
Article copyright: © Copyright 1972 American Mathematical Society

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