Orthogonality of the Ferrers' Associated Legendre Functions of the Second Kind with Imaginary Argument
arXiv:1701.02219
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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