The scaling properties and the multiple derivative of Legendre polynomials
Classical Analysis and ODEs
2017-11-06 v1
Abstract
In this paper, we study the scaling properties of Legendre polynomials Pn(x). We show that Pn(ax), where a is a constant, can be expanded as a sum of either Legendre polynomials Pn(x) or their multiple derivatives dkPn(x)/dxk, and we derive a general expression for the expansion coefficients. In addition, we demonstrate that the multiple derivative dkPn(x)/dxk can also be expressed as a sum of Legendre polynomials and we obtain a recurrence relation for the coefficients.
Keywords
Cite
@article{arxiv.1711.00925,
title = {The scaling properties and the multiple derivative of Legendre polynomials},
author = {Guillaume Marc Laurent and Geoffrey Robert Harrison},
journal= {arXiv preprint arXiv:1711.00925},
year = {2017}
}
Comments
7 pages