Inequalities and asymptotic expansions associated with the Wallis sequence

Journal of inequalities and applications

Long Lin¹ 

关键词: Wallis sequence;    gamma function;    psi function;    polygamma function;    inequality;    asymptotic expansion;   

DOI  :  10.1186/1029-242X-2014-251

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We present the asymptotic expansions of functions involving the ratio of gamma functions and provide formulas for determining the coefficients of the asymptotic expansions. As consequences, we obtain the asymptotic expansions of the Wallis sequence. Also, we establish inequalities for the Wallis sequence. MSC:40A05, 33B15, 41A60, 26D15.

【 授权许可】

CC BY