Fourier Transform of some irrational integrands

2019/12/14 by Laurenzi, Bernard J.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1912.06885

Abstract

Fourier sine transforms containing irrational integrands are presented. Explicit closed form expressions are shown to be related to Lommel functions and in special cases to the Fresnel integrals. Such integrals arise in the semi-classical theory of the Chemical Potential of the atomic elements.

Related

• Some Conditions for Existence and Integrability of the Fourier Transform
• Special values of the Lommel functions and associated integrals
• Some integrals related to the Fermi function
• A Generalization of Fourier Series occurring in Atomic Theory
• Integrability of the Fourier transform: functions of bounded variation