English

Discrete Fourier-Jacobi transform

Classical Analysis and ODEs 2020-08-07 v1

Abstract

Discrete analogs of the classical Fourier-Jacobi transform are introduced and investigated. It involves series and integrals with respect to parameters of the Gauss hypergeometric function 2F1(a+in/2,ain/2; c;x2), x>0,nN,a,c>0,i{}_2F_1(a+in/2,a-in/2;\ c; -x^2 ), \ x >0, n \in \mathbb{N}, a,c > 0, i is the imaginary unit. The corresponding inversion formulas for suitable functions and sequences in terms of these series and integrals are established.

Keywords

Cite

@article{arxiv.2008.02561,
  title  = {Discrete Fourier-Jacobi transform},
  author = {Semyon Yakubovich},
  journal= {arXiv preprint arXiv:2008.02561},
  year   = {2020}
}
R2 v1 2026-06-23T17:40:42.187Z