English

Limits of Jensen polynomials for partitions and other sequences

Combinatorics 2021-08-17 v1 Number Theory

Abstract

It was discovered recently by Griffin, Ono, Rolen and Zagier that the Jensen polynomials associated to many sequences have Hermite polynomial limits. We develop this theory in detail, based on the log-polynomial property which is a refinement of log-concavity and log-convexity. Applications to various partition sequences are given. An application to the sequence of factorials leads naturally to evaluating limits of generalized Laguerre polynomials.

Keywords

Cite

@article{arxiv.2108.06775,
  title  = {Limits of Jensen polynomials for partitions and other sequences},
  author = {Cormac O'Sullivan},
  journal= {arXiv preprint arXiv:2108.06775},
  year   = {2021}
}

Comments

20 pages, 1 figure