Sharp inequalities and asymptotic expansion associated with the Wallis sequence

Journal of inequalities and applications

Ji-En Deng¹ 

关键词: Wallis sequence;    gamma function;    psi function;    polygamma function;    inequality;    asymptotic expansion;    40A05;    33B15;    41A60;    26D15;   

DOI  :  10.1186/s13660-015-0699-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We present asymptotic expansion of function involving the ratio of gamma functions and provide a recurrence relation for determining the coefficients of the asymptotic expansion. As a consequence, we obtain asymptotic expansion of the Wallis sequence. Also, we establish sharp inequalities for the Wallis sequence.

【 授权许可】

CC BY