| A Note on the Property of ψ-Function |
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| 基金项目： | Supported by the National Natural Science Foundation of China (10926128) |
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| 摘 要： | About the accurate value of ψ ( x ) = Γ′ ( x ) / Γ ( x), we know only ψ (1)and ψ (1/ 2).In this paper, by calculating the accurate values of some series expansion of a function and applying some skills of complex analysis, we prove that the expression of the ψ-function admits a finite expression in elementary function for rational number z. As an application, some examples are given.
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| 关 键 词： | ψ-function Γ-function Euler’s constant |
A note on the property of <Emphasis Type="Italic">ψ</Emphasis>-function |
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| Authors: | Zitian Xie Qinghua Zhou |
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| Institution: | XIE Zitian,ZHOU Qinghua Department of Mathematics,Zhaoqing University,Zhaoqing 526061,Guangdong,China |
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| Abstract: | About the accurate value of ψ(x) = Γ′(x)=Γ′(x)/Γ(x), we know only ψ(1) and ψ(1/2). In this paper, by calculating the accurate values of some series expansion of a function and applying some skills of
complex analysis, we prove that the expression of the ψ-function admits a finite expression in elementary function for rational number z. As an application, some examples are given. |
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| Keywords: | ψ-function Γ-function Euler’s constant |
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