Zernike圆多项式与包含Bessel函数乘积的无穷积分
Zernike circle polynomials and infinite integrals involving the product of Bessel functions
摘要：
与泽尼克圆多项式有关的几个量允许将表达式表示为涉及两个或三个贝塞尔函数的乘积的无穷积分。在本文中，这些积分被明确地识别和计算为（a）缩放和移位的圆多项式的展开系数，（b）两个圆多项式的相关的展开系数，（c）圆多项式的余弦表示中出现的傅立叶系数，（d）由于活塞上的不均匀速度分布而引起的折流活塞声辐射器的瞬态响应。
英文摘要：
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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