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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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences
Main Author: Paul W. Haggard
Format: Article
Language:English
Published: Wiley 1985-01-01
Subjects:
associated Legendre functions
Legendre polynomials
series of Legendre numbers
integrals of Legendre polynomials
orthogonal set
derivatives of Legendre polynomials.
Online Access:http://dx.doi.org/10.1155/S0161171285000436
Description
Summary: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.
ISSN:0161-1712
1687-0425

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