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arXiv · 1701.02219

Orthogonality of the Ferrers' Associated Legendre Functions of the Second Kind with Imaginary Argument

N. Dimakis
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Abstract

In this work we study the associated Legendre functions of the second kind with a purely imaginary argument $Q^k_\ell(\mathbb{i}\, x)$. We derive the conditions under which they provide a set of square integrable functions when $x \in \mathbb{R}$ and we prove the relevant orthogonality relation that they satisfy.

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N. Dimakis. 2017-01-09. Orthogonality of the Ferrers' Associated Legendre Functions of the Second Kind with Imaginary Argument. https://arxiv.org/abs/1701.02219

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