ABSTRACT In this article we establish a sharp two-sided inequality for bounding the Wallis ratio.... more 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. MSC: 11B65, 41A44, 05A10, 26D20, 33B15, 41A60.
ABSTRACT In this article, we present a necessary condition and a necessary and sufficient conditi... more ABSTRACT In this article, we present a necessary condition and a necessary and sufficient condition for a class of functions to be completely monotonic. MSC: 34A40, 26D10, 26A48.
In the present paper, the authors establish necessary and sufficient conditions for the functions... more In the present paper, the authors establish necessary and sufficient conditions for the functions $x^\alpha\bigl\lvert\psi^{(i)}(x+\beta)\bigr\lvert$ and $\alpha\bigl\lvert\psi^{(i)}(x+\beta)\bigr\lvert-x\bigl\lvert\psi^{(i+1)}(x+\beta)\bigr\lvert$ respectively to be monotonic and completely monotonic on $(0,\infty)$, where $i\in\mathbb{N}$, $\alpha>0$ and $\beta\ge0$ are scalars, and $\psi^{(i)}(x)$ are polygamma functions.
ABSTRACT In this article we establish a sharp two-sided inequality for bounding the Wallis ratio.... more 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. MSC: 11B65, 41A44, 05A10, 26D20, 33B15, 41A60.
ABSTRACT In this article, we present a necessary condition and a necessary and sufficient conditi... more ABSTRACT In this article, we present a necessary condition and a necessary and sufficient condition for a class of functions to be completely monotonic. MSC: 34A40, 26D10, 26A48.
In the present paper, the authors establish necessary and sufficient conditions for the functions... more In the present paper, the authors establish necessary and sufficient conditions for the functions $x^\alpha\bigl\lvert\psi^{(i)}(x+\beta)\bigr\lvert$ and $\alpha\bigl\lvert\psi^{(i)}(x+\beta)\bigr\lvert-x\bigl\lvert\psi^{(i+1)}(x+\beta)\bigr\lvert$ respectively to be monotonic and completely monotonic on $(0,\infty)$, where $i\in\mathbb{N}$, $\alpha>0$ and $\beta\ge0$ are scalars, and $\psi^{(i)}(x)$ are polygamma functions.
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Papers by Senlin Guo