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Nijimbere, V. (2020) Analytical Evaluation of Non-Elementary Integrals Involving Some Exponential, Hyperbolic and Trigonometric Elementary Functions and Derivation of New Probability Measures Generalizing the Gamma-Type and Gaussian-Type Distributions. Advances in Pure Mathematics, 10, 371-392.
https://doi.org/10.4236/apm.2020.107023

has been cited by the following article:

• TITLE: Analytical Solutions to Definite Integrals for Combinations of Legendre, Bessel and Trigonometric Functions Encountered in Propagation and Scattering Problems in Spherical Coordinates

  AUTHORS: Farhad Azadi Namin

  KEYWORDS: Mie Theory, Vector Spherical Wave Function, Eigen-Function Expansion, Spherical Harmonics, Special Functions

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.9, September 20, 2022

  ABSTRACT: Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in terms of spherical which in turn requires evaluation of certain definite integrals whose integrands are products of Bessel functions, associated Legendre functions and periodic functions. Here we present analytical results for two specific integrals that are encountered in expansion of arbitrary fields in terms of summation of spherical waves. The analytical results are in terms of finite summations which include Lommel functions. A concise analytical expression is also derived for the special case of Lommel functions that arise, rendering expensive numerical integration or other iterative techniques unnecessary.