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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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Uniform asymptotic expansions of the Jacobi polynomials and an associated function
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by David Elliott PDF
Math. Comp. 25 (1971), 309-315 Request permission

Abstract:

Asymptotic expansions have been obtained using two theorems due to Olver for the Jacobi polynomials and an associated function. These expansions are uniformly valid for complex arguments over certain regions, for large values of the order.
References
    J. D. Donaldson & David Elliott, Quadrature II: The Estimation of Remainders in Certain Quadrature Rules, University of Tasmania, Mathematics Department, Technical Report No. 24, February, 1970. A. Erdélyi, W. Magnus, D. Oberhettinger & D. G. Tricomi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York, 1953. MR 15, 419. A. Erdélyi, W. Magnus, D. Oberhettinger & D. G. Tricomi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953. MR 15, 419.
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  • F. W. J. Olver, The asymptotic solution of linear differential equations of the second order in a domain containing one transition point, Philos. Trans. Roy. Soc. London Ser. A 249 (1956), 65–97. MR 79157, DOI 10.1098/rsta.1956.0015
  • G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1939. MR 1, 14.
  • F. G. Tricomi and A. Erdélyi, The asymptotic expansion of a ratio of gamma functions, Pacific J. Math. 1 (1951), 133–142. MR 43948
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 309-315
  • MSC: Primary 33A65
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0294737-5
  • MathSciNet review: 0294737