Asian Research Journal of Mathematics

Asymptotic Expansions Related to the Wallis Ratio Based on the Bell Polynomials

Aimin Xu *

Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, China.

*Author to whom correspondence should be addressed.

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Abstract

In this paper, we establish a new asymptotic expansion related to the Wallis ratio. By using the exponential Bell polynomials, we show that the coefficients of the asymptotic expansion can be recursively determined. In addition, an explicit expression for the coefficients is given. Our results improve and generalize the existing ones [1].

Keywords: Wallis ratio, Asymptotic expansion, Bell polynomial

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