Evaluation of integrals involving orthogonal polynomials: Laguerre polynomial and Bessel function example

A. D. Alhaidari

doi:10.1016/j.aml.2006.02.020

Evaluation of integrals involving orthogonal polynomials: Laguerre polynomial and Bessel function example

A. D. Alhaidari^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

6 Scopus citations

Abstract

Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a new method for evaluating integrals that include orthogonal polynomials. The method is illustrated by obtaining the following integral result that involves the Bessel function and associated Laguerre polynomial: {Mathematical expression} where μ and ν are real parameters such that μ ≥ 0 and ν > - frac(1, 2), cos θ = frac(μ² - 1 / 4, μ² + 1 / 4), and C_n^λ (x) is a Gegenbauer (ultraspherical) polynomial.

Original language	English
Pages (from-to)	38-42
Number of pages	5
Journal	Applied Mathematics Letters
Volume	20
Issue number	1
DOIs	https://doi.org/10.1016/j.aml.2006.02.020
State	Published - Jan 2007

Keywords

Associated Laguerre polynomial
Bessel function
Definite integrals
Function spectral decomposition
Gegenbauer polynomial
Recursion relation

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2006.02.020

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title = "Evaluation of integrals involving orthogonal polynomials: Laguerre polynomial and Bessel function example",

abstract = "Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a new method for evaluating integrals that include orthogonal polynomials. The method is illustrated by obtaining the following integral result that involves the Bessel function and associated Laguerre polynomial: \{Mathematical expression\} where μ and ν are real parameters such that μ ≥ 0 and ν > - frac(1, 2), cos θ = frac(μ2 - 1 / 4, μ2 + 1 / 4), and Cnλ (x) is a Gegenbauer (ultraspherical) polynomial.",

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author = "Alhaidari, \{A. D.\}",

year = "2007",

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doi = "10.1016/j.aml.2006.02.020",

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T1 - Evaluation of integrals involving orthogonal polynomials

T2 - Laguerre polynomial and Bessel function example

AU - Alhaidari, A. D.

PY - 2007/1

Y1 - 2007/1

N2 - Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a new method for evaluating integrals that include orthogonal polynomials. The method is illustrated by obtaining the following integral result that involves the Bessel function and associated Laguerre polynomial: {Mathematical expression} where μ and ν are real parameters such that μ ≥ 0 and ν > - frac(1, 2), cos θ = frac(μ2 - 1 / 4, μ2 + 1 / 4), and Cnλ (x) is a Gegenbauer (ultraspherical) polynomial.

AB - Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a new method for evaluating integrals that include orthogonal polynomials. The method is illustrated by obtaining the following integral result that involves the Bessel function and associated Laguerre polynomial: {Mathematical expression} where μ and ν are real parameters such that μ ≥ 0 and ν > - frac(1, 2), cos θ = frac(μ2 - 1 / 4, μ2 + 1 / 4), and Cnλ (x) is a Gegenbauer (ultraspherical) polynomial.

KW - Associated Laguerre polynomial

KW - Bessel function

KW - Definite integrals

KW - Function spectral decomposition

KW - Gegenbauer polynomial

KW - Recursion relation

UR - https://www.scopus.com/pages/publications/33750026703

U2 - 10.1016/j.aml.2006.02.020

DO - 10.1016/j.aml.2006.02.020

M3 - Article

AN - SCOPUS:33750026703

SN - 0893-9659

VL - 20

SP - 38

EP - 42

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 1

ER -

Evaluation of integrals involving orthogonal polynomials: Laguerre polynomial and Bessel function example

Abstract

Keywords

ASJC Scopus subject areas

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