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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Uniform asymptotic expansions of the Jacobi polynomials and an associated function


Author: David Elliott
Journal: Math. Comp. 25 (1971), 309-315
MSC: Primary 33A65
MathSciNet review: 0294737
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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 [Enhancements On Off] (What's this?)

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  • [2] A. Erdélyi, W. Magnus, D. Oberhettinger & D. G. Tricomi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York, 1953. MR 15, 419.
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  • [6] 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 0079157 (18,38f)
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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1971-0294737-5
PII: S 0025-5718(1971)0294737-5
Keywords: Uniform asymptotic expansions, Jacobi polynomials, hypergeometric function, complex plane, Olver's theorems, modified Bessel functions
Article copyright: © Copyright 1971 American Mathematical Society