Bessel integrals in epsilon expansion: Squared spherical Bessel functions averaged with Gaussian power-law distributions
作者：
Highlights：
• The high-index evaluation of integrals containing squared spherical Bessel functions is studied.
• The integrals arise as spectral averages in multipole expansions of spherical Gaussian random fields.
• A high-precision integration technique based on finite Hankel series in epsilon regularization is developed.
• An Airy approximation of the integrals is derived using uniform Nicholson asymptotics.
• The finite series evaluation is compared with the Airy approximation over an extended range of Bessel indices.
摘要
•The high-index evaluation of integrals containing squared spherical Bessel functions is studied.•The integrals arise as spectral averages in multipole expansions of spherical Gaussian random fields.•A high-precision integration technique based on finite Hankel series in epsilon regularization is developed.•An Airy approximation of the integrals is derived using uniform Nicholson asymptotics.•The finite series evaluation is compared with the Airy approximation over an extended range of Bessel indices.
论文关键词：Squared spherical Bessel functions,Regularization of Hankel series,Gaussian power-law densities,Kummer distributions,Airy approximation of Bessel integrals
论文评审过程：Available online 15 October 2013.
论文官网地址：https://doi.org/10.1016/j.amc.2013.09.035
