On Legendre numbers

The Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series of Legendre numbers and evaluating certain in...

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Main Author: Paul W. Haggard
Format: Article
Language:English
Published: Wiley 1985-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171285000436
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author Paul W. Haggard
author_facet Paul W. Haggard
author_sort Paul W. Haggard
collection DOAJ
description The Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series of Legendre numbers and evaluating certain integrals. Legendre numbers are used to obtain the derivatives of all orders of the Legendre polynomials at x=1.
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institution Kabale University
issn 0161-1712
1687-0425
language English
publishDate 1985-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-6d2cdbe1265e4c2eb38dfc26660d3f7a2025-02-03T01:21:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018240741110.1155/S0161171285000436On Legendre numbersPaul W. Haggard0Department of Mathematics, East Carolina University, Greenville 27834, North Carolina, USAThe Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series of Legendre numbers and evaluating certain integrals. Legendre numbers are used to obtain the derivatives of all orders of the Legendre polynomials at x=1.http://dx.doi.org/10.1155/S0161171285000436associated Legendre functionsLegendre polynomialsseries of Legendre numbersintegrals of Legendre polynomialsorthogonal setderivatives of Legendre polynomials.
spellingShingle Paul W. Haggard
On Legendre numbers
International Journal of Mathematics and Mathematical Sciences
associated Legendre functions
Legendre polynomials
series of Legendre numbers
integrals of Legendre polynomials
orthogonal set
derivatives of Legendre polynomials.
title On Legendre numbers
title_full On Legendre numbers
title_fullStr On Legendre numbers
title_full_unstemmed On Legendre numbers
title_short On Legendre numbers
title_sort on legendre numbers
topic associated Legendre functions
Legendre polynomials
series of Legendre numbers
integrals of Legendre polynomials
orthogonal set
derivatives of Legendre polynomials.
url http://dx.doi.org/10.1155/S0161171285000436
work_keys_str_mv AT paulwhaggard onlegendrenumbers