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arXiv · 0910.4715

Some differentiation formulas for Legendre polynomials

Radoslaw Szmytkowski
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Abstract

In a series of recent works, we have provided a number of explicit expressions for the derivative of the associated Legendre function of the first kind with respect to its degree, $[\partial P_ν^{m}(z)/\partialν]_{ν=n}$, with $m,n\in\mathbb{N}$. In this communication, we use some of those expressions to obtain several, we believe new, explicit formulas for the derivatives $\mathrm{d}^{m}[P_{n}(z)\ln(z\pm1)]/\mathrm{d}z^{m}$, where $P_{n}(z)$ is the Legendre polynomial.

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Radoslaw Szmytkowski. 2009-10-25. Some differentiation formulas for Legendre polynomials. https://arxiv.org/abs/0910.4715

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