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

Abstract

The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, e d x

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

“…These inner products are definite double integrals where the integrands are products of special functions. With very few exceptions [4] [5] [6] these integrals are intractable and have to be evaluated using quadrature methods which itself presents a degree of difficulty due to the fact that evaluating special function can be a computationally expensive task.…”