On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas

Chao-Ping Chen and Richard B. Paris

Applied Mathematics and Computation, 2017, vol. 293, issue C, 30-39

Abstract: For all integers n ≥ 1, let Wn(p,q)=∏j=1n{e−p/j(1+pj+qj2)}and Rn(p,q)=∏j=1n{e−p/(2j−1)(1+p2j−1+q(2j−1)2)},where p, q are complex parameters. The infinite product W∞(p, q) includes the Wallis and Wilf formulas, and also the infinite product definition of Weierstrass for the gamma function, as special cases. In this paper, we present asymptotic expansions of Wn(p, q) and Rn(p, q) as n → ∞. In addition, we also establish asymptotic expansions for the Wallis sequence.

Keywords: Gamma function; Psi function; Euler–Mascheroni constant; Asymptotic expansion; Wallis sequence (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300316304982
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:293:y:2017:i:c:p:30-39

DOI: 10.1016/j.amc.2016.08.003

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().