Curious identities involving Legendre polynomials and Apéry-like numbers

Li-Li Cui; Zhi-Hong Sun

Curious identities involving Legendre polynomials and Apéry-like numbers

Number Theory 2026-07-14 v1 Classical Analysis and ODEs Combinatorics

Authors: Li-Li Cui , Zhi-Hong Sun

Abstract

In this paper, we establish some curious identities involving Legendre polynomials and the first kind of Ap\'ery-like numbers. As applications, many new supercongruences are deduced.

Keywords

Legendre polynomials Apéry-like numbers supercongruences identities

Cite

@article{arxiv.2607.12330,
  title  = {Curious identities involving Legendre polynomials and Apéry-like numbers},
  author = {Li-Li Cui and Zhi-Hong Sun},
  journal= {arXiv preprint arXiv:2607.12330},
  year   = {2026}
}

Comments

25 pages