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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A family of generalized Jacobi polynomials
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by F. Locher PDF
Math. Comp. 53 (1989), 303-309 Request permission

Abstract:

The family of orthogonal polynomials corresponding to a generalized Jacobi weight function was considered by Wheeler and Gautschi who derived recurrence relations, both for the related Chebyshev moments and for the associated orthogonal polynomials. We obtain an explicit representation of these polynomials, from which the recurrence relation can be derived.
References
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  • T. S. Chihara, An introduction to orthogonal polynomials, Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York-London-Paris, 1978. MR 0481884
  • Walter Gautschi, On some orthogonal polynomials of interest in theoretical chemistry, BIT 24 (1984), no. 4, 473–483. MR 764820, DOI 10.1007/BF01934906
  • B. Lenze and F. Locher, Jacobi moments and a family of special orthogonal polynomials, Numerical integration, III (Oberwolfach, 1987) Internat. Schriftenreihe Numer. Math., vol. 85, Birkhäuser, Basel, 1988, pp. 99–110. MR 1021527
  • G. Szegö, Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, 1975. J. C. Wheeler, "Modified moments and continued fraction coefficients for the diatomic linear chain," J. Chem. Phys., v. 80, 1984, pp. 472-476.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 303-309
  • MSC: Primary 33A65
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0968151-4
  • MathSciNet review: 968151