A remarkable identity involving bessel functions

Diego E. Dominici; Peter M.W. Gill; Taweetham Limpanuparb

doi:10.1098/rspa.2011.0664

A remarkable identity involving bessel functions

Diego E. Dominici^*, Peter M.W. Gill, Taweetham Limpanuparb

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and the integrand are of exactly the same form and the sum converges to the integral relatively fast for most cases. A proof and numerical examples of the identity are discussed.

Original language	English
Pages (from-to)	2667-2681
Number of pages	15
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	468
Issue number	2145
DOIs	https://doi.org/10.1098/rspa.2011.0664
Publication status	Published - 8 Sept 2012

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title = "A remarkable identity involving bessel functions",

abstract = "We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and the integrand are of exactly the same form and the sum converges to the integral relatively fast for most cases. A proof and numerical examples of the identity are discussed.",

keywords = "Bessel functions, Coulomb operator, Hypergeometric functions",

author = "Dominici, {Diego E.} and Gill, {Peter M.W.} and Taweetham Limpanuparb",

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T1 - A remarkable identity involving bessel functions

AU - Dominici, Diego E.

AU - Gill, Peter M.W.

AU - Limpanuparb, Taweetham

PY - 2012/9/8

Y1 - 2012/9/8

N2 - We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and the integrand are of exactly the same form and the sum converges to the integral relatively fast for most cases. A proof and numerical examples of the identity are discussed.

AB - We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and the integrand are of exactly the same form and the sum converges to the integral relatively fast for most cases. A proof and numerical examples of the identity are discussed.

KW - Bessel functions

KW - Coulomb operator

KW - Hypergeometric functions

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U2 - 10.1098/rspa.2011.0664

DO - 10.1098/rspa.2011.0664

M3 - Article

SN - 1364-5021

VL - 468

SP - 2667

EP - 2681

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2145

ER -

A remarkable identity involving bessel functions

Abstract

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