Abstract
In this article we establish a sharp two-sided inequality for bounding the Wallis ratio. Some best constants for the estimation of the Wallis ratio are obtained. An asymptotic formula for the Wallis ratio is also presented.
Highlights
Introduction and main resultsFor n ∈ N, the double factorial n!! is defined by (n– )/ n!! = (n – i), ( ) i=where in ( ) the floor function t denotes the largest integer less than or equal to t
In what follows, we denote the ratio of two neighboring double factorials by ( n – )!!
Our main result may be stated as the following theorem
Summary
In what follows, we denote the ratio of two neighboring double factorials by ( n – )!! The Wallis ratio Wn can be represented as follows Where in ( ) (x) is the classical Euler’s gamma function defined for x > by In [ ] the author proved, for all n ∈ N,
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