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

Abstract

In this work we study the associated Legendre functions of the second kind with a purely imaginary argument $Q_{\ell }^k(ix)$. 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.

arXiv comment10 pages, 0 Figures