Fourier transform of a Bessel function multiplied by a Gaussian

2013/10/30 by Michael Jabara Carley, Carley, Michael
Earth and Planetary Sciences · Engineering · #Acoustic Wave Phenomena Research #Aerodynamics and Acoustics in Jet Flows #FOS: Physical sciences #Mathematical Physics (math-ph) #Seismic Waves and Analysis

paper · pdf · doi:10.48550/arxiv.1310.8269

openalex publication_date 2013/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An analytical result is given for the exact evaluation of an integral which arises in the analysis of acoustic radiation from wave packet sources: I_mn(β,q) = ∫_-∞^∞ e^-β²x²-i q xx^m+1/2J_n+1/2(x) d x, where m and n are non-negative integers, and J_n+1/2(⋅) is a Bessel function of order n+1/2.

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