Properties of the polynomials associated with the Jacobi polynomials
Author:
S. Lewanowicz
Journal:
Math. Comp. 47 (1986), 669682
MSC:
Primary 33A65; Secondary 33A45
MathSciNet review:
856711
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: Power forms and Jacobi polynomial forms are found for the polynomials associated with Jacobi polynomials. Also, some differentialdifference equations and evaluations of certain integrals involving are given.
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MR 727118
(85f:65001)
 [1]
 R. Askey & G. Gasper, "Jacobi polynomial expansions of Jacobi polynomials with nonnegative coefficients," Proc. Cambridge Philos. Soc., v. 70, 1971, pp. 243255. MR 0296369 (45:5430)
 [2]
 R. Askey & J. Wimp, "Associated Laguerre and Hermite polynomials," Proc. Roy. Soc. Edinburgh Sect. A, v. 96, 1984, pp. 1537. MR 741641 (85f:33014)
 [3]
 P. Barrucand & D. Dickinson, "On the associated Legendre polynomials," in Orthogonal Expansions and Their Continuous Analogues (D. T. Haimo, ed.), Southern Illinois Univ. Press, Carbondale, Ill., 1967, pp. 4350. MR 0232975 (38:1298)
 [4]
 J. Bustoz & M. E. H. Ismail, "The associated ultraspherical polynomials and their qanalogues," Canad. J. Math., v. 34, 1982, pp. 718736. MR 663314 (84c:33013)
 [5]
 A. Erdélyi et al., Higher Transcendental Functions, Vols. 1 and 2, McGrawHill, New York, 1953.
 [6]
 W. Gautschi, "Minimal solutions of threeterm recurrence relations and orthogonal polynomials," Math. Comp., v. 36, 1981, pp. 547554. MR 606512 (82m:33006)
 [7]
 C. C. Grosjean, "The orthogonality property of the Lommel polynomials and a twofold infinity of relations between Rayleigh's sums," J. Comput. Appl. Math., v. 10, 1984, pp. 355382. MR 755809 (85m:33011)
 [8]
 C. C. Grosjean, "Theory of recursive generation of systems of orthogonal polynomials: An illustrative example," J. Comput. Appl. Math., v. 12/13, 1985, pp. 299318. MR 793963 (86g:33015)
 [9]
 C. C. Grosjean, private communication, 1985.
 [10]
 S. L. Kalla, S. Conde & Y. L. Luke, "Integrals of Jacobi functions," Math. Comp., v. 39, 1982, pp. 207214. MR 637298 (83a:33005)
 [11]
 S. Lewanowicz, "Recurrence relations for hypergeometric functions of unit argument," Math. Comp., v. 45, 1985, pp. 521535. MR 804941 (86m:33004)
 [12]
 S. Lewanowicz, "Recurrence relations for the coefficients in Jacobi series solutions of linear differential equations," SIAM J. Math. Anal., v. 17, 1986. (To appear.) MR 853515 (87k:33011)
 [13]
 Y. L. Luke, Mathematical Functions and Their Approximations, Academic Press, New York, 1975. MR 0501762 (58:19039)
 [14]
 P. Nevai, "A new class of orthogonal polynomials," Proc. Amer. Math. Soc., v. 91, 1984, pp. 409415. MR 744640 (85f:42036)
 [15]
 S. Paszkowski, Polynômes Associés aux Polynômes Orthogonaux Classiques, Publication ANO136, Univ. Sci. Tech. de Lille, U.E.R. d'I.E.E.A., 1984.
 [16]
 E. D. Rainville, Special Functions, Macmillan, New York, 1960. MR 0107725 (21:6447)
 [17]
 L. J. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. MR 0201688 (34:1570)
 [18]
 G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1939.
 [19]
 J. Wimp, Computation with Recurrence Relations, Pitman, Boston, 1984. MR 727118 (85f:65001)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198608567118
PII:
S 00255718(1986)08567118
Article copyright:
© Copyright 1986 American Mathematical Society
