English

Asymptotics of a ${}_3F_2$ polynomial associated with the Catalan-Larcombe-French sequence

Classical Analysis and ODEs 2016-09-07 v1

Abstract

The large nn behaviour of the hypergeometric polynomial \FFFn\sfrac12\sfrac12\sfrac12n\sfrac12n1\FFF{-n}{\sfrac12}{\sfrac12}{\sfrac12-n}{\sfrac12-n}{-1} is considered by using integral representations of this polynomial. This 3F2{}_3F_2 polynomial is associated with the Catalan-Larcombe-French sequence. Several other representations are mentioned, with references to the literature, and another asymptotic method is described by using a generating function of the sequence. The results are similar to those obtained by Clark (2004) who used a binomial sum for obtaining an asymptotic expansion.

Keywords

Cite

@article{arxiv.math/0610191,
  title  = {Asymptotics of a ${}_3F_2$ polynomial associated with the Catalan-Larcombe-French sequence},
  author = {Nico M. Temme},
  journal= {arXiv preprint arXiv:math/0610191},
  year   = {2016}
}

Comments

10 pages, 1 figure. Accepted for publication in {\em Analysis and Applications}