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arXiv · 1910.08394

Discrete Mehler-Fock transforms

Semyon Yakubovich
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Abstract

Discrete analogs of the classical Mehler-Fock transforms are introduced and investigated. It involves series with the associated Legendre function $P^μ_{in-1/2}(x), x > 1,\ {\rm Re} μ< 1/2, \ n \in \mathbb{N}, i $ is the imaginary unit, and the so-called incomplete Legendre integrals. Several expansions of arbitrary functions and sequences in terms of these series and integrals are established.

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Semyon Yakubovich. 2019-10-18. Discrete Mehler-Fock transforms. https://arxiv.org/abs/1910.08394

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