Article ID Journal Published Year Pages File Type
4625553 Applied Mathematics and Computation 2017 10 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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