Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 077, 10 pages      arXiv:1210.0041      https://doi.org/10.3842/SIGMA.2012.077
Contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”

Definite Integrals using Orthogonality and Integral Transforms

Howard S. Cohl a and Hans Volkmer b
a) Applied and Computational Mathematics Division, Information Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, 20899-8910, USA
b) Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI, 53201, USA

Received July 31, 2012, in final form October 15, 2012; Published online October 19, 2012

Abstract
We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.

Key words: definite integrals; associated Legendre functions; Bessel functions; Chebyshev polynomials of the first kind.

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