Mathematics – Classical Analysis and ODEs
Scientific paper
2006-10-05
Mathematics
Classical Analysis and ODEs
10 pages, 1 figure. Accepted for publication in {\em Analysis and Applications}
Scientific paper
The large $n$ behaviour of the hypergeometric polynomial $$\FFF{-n}{\sfrac12}{\sfrac12}{\sfrac12-n}{\sfrac12-n}{-1}$$ is considered by using integral representations of this polynomial. This ${}_3F_2$ 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.
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