Zernike circle polynomials and infinite integrals involving the product of Bessel functions

Details Zernike circle polynomials and infinite integrals involving the product of Bessel functions Zernike circle polynomials and infinite integrals involving the product of Bessel functions

2010-07-05

arxiv.org/abs/1007.0667v1

Physics

Mathematical Physics

Scientific paper

Several quantities related to the Zernike circle polynomials admit an expression as an infinite integral involving the product of two or three Bessel functions. In this paper these integrals are identified and evaluated explicitly for the cases of (a) the expansion coefficients of scaled-and-shifted circle polynomials, (b) the expansion coefficients of the correlation of two circle polynomials, (c) the Fourier coefficients occurring in the cosine representation of the circle polynomials, (d) the transient response of a baffled-piston acoustical radiator due to a non-uniform velocity profile on the piston.

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