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

 

On finite integrals involving trigonometric, Bessel, and Legendre functions


Author: Richard L. Lewis
Journal: Math. Comp. 23 (1969), 259-273
MSC: Primary 65.25
MathSciNet review: 0242350
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Abstract: A finite integral involving the product of powers of trigonometric functions, up to two associated Legendre functions, and zero or one Bessel function is evaluated. When certain combinations of the otherwise complex function parameters are integers, the resulting expression becomes greatly simplified. So restricting the parameters, this still quite general case may be transformed into four canonical forms, each of which admits rapid convergence of the only nonterminating series in the expressions. Finally, closed form expressions are obtained for a number of special cases.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1969-0242350-9
PII: S 0025-5718(1969)0242350-9
Keywords: Finite Integrals, Bessel Functions, Legendre Functions, Generalized Hypergeometric Functions
Article copyright: © Copyright 1969 American Mathematical Society