English

Discrete Mehler-Fock transforms

Classical Analysis and ODEs 2019-10-21 v1

Abstract

Discrete analogs of the classical Mehler-Fock transforms are introduced and investigated. It involves series with the associated Legendre function Pin1/2μ(x),x>1, Reμ<1/2, nN,iP^\mu_{in-1/2}(x), x > 1,\ {\rm Re} \mu < 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.

Keywords

Cite

@article{arxiv.1910.08394,
  title  = {Discrete Mehler-Fock transforms},
  author = {Semyon Yakubovich},
  journal= {arXiv preprint arXiv:1910.08394},
  year   = {2019}
}
R2 v1 2026-06-23T11:47:47.254Z