Asian Research Journal of Mathematics

Some New Optimal Bounds for Wallis Ratio

Yin Chen *

Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada.

*Author to whom correspondence should be addressed.

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Abstract

Wallis ratio can be expressed as an asymptotic expansion using Stirling series and Bernoulli numbers. We prove the general inequalities for Wallis ratio for arbitrary number of terms in the asymptotic expansion. We show that the coefficients in the asymptotic expansion are the best possible.

Keywords: Wallis ratio, bernoulli numbers, stirling series

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