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On Finite Integrals Involving Trigonometric, Bessel, and Legendre Functions

1969
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Mathematics of Computation
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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

doi:10.2307/2004421
fatcat:g43xrq3zzvcpzatsbszmgb7may