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

C. -P. Chen, R. B. Paris

For all integers $n\ge 1$, let \begin{align*} W_n(p,q)=\prod_{j=1}^{n}\left\{e^{-p/j}\left(1+\frac{p}{j}+\frac{q}{j^2}\right)\right\} \end{align*} and \begin{align*} R_n(p, q)=\pro…