三维傅里叶变换，球面贝塞尔函数积分和新的δ函数恒等式
Three-dimensional Fourier transforms, integrals of spherical Bessel functions, and novel delta function identities
摘要：
我们提出了一个通用的方法来评估各种各样的三维傅立叶变换。所考虑的变换包括库仑势和偶极势的有用情况，并且包括变换是奇异的并且涉及与狄拉克δ函数成比例的项的情况。我们的方法利用瑞利展开的exp（ipr）的球面贝塞尔函数，我们研究了一些积分，包括奇异积分，涉及的权力的独立变量倍的球面贝塞尔函数。我们使用我们的方法通过几个三维傅立叶变换的例子，并展示如何推导出一些涉及1/r，1/r^2和delta（\vec r）的多个导数的恒等式。
英文摘要：
We present a general approach for evaluating a large variety of three-dimensional Fourier transforms. The transforms considered include the useful cases of the Coulomb and dipole potentials, and include situations where the transforms are singular and involve terms proportional to the Dirac delta function. Our approach makes use of the Rayleigh expansion of exp(i p.r) in terms of spherical Bessel functions, and we study a number of integrals, including singular integrals, involving a power of the independent variable times a spherical Bessel function. We work through several examples of three-dimensional Fourier transforms using our approach and show how to derive a number of identities involving multiple derivatives of 1/r, 1/r^2, and delta(\vec r).
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