International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 407-411
doi:10.1155/S0161171285000436
Research notes
On Legendre numbers
Department of Mathematics, East Carolina University, Greenville 27834, North Carolina, USA
Received 7 February 1984
Copyright © 1985 Paul W. Haggard. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.