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arXiv · 1711.00925

The scaling properties and the multiple derivative of Legendre polynomials

Guillaume Marc Laurent·Geoffrey Robert Harrison
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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.

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Guillaume Marc Laurent, Geoffrey Robert Harrison. 2017-10-28. The scaling properties and the multiple derivative of Legendre polynomials. https://arxiv.org/abs/1711.00925

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