关于lgΓ(x)的Kummer-Fourier级数研究

On Kummer-Fourier Series for lgΓ(x)

采用初等数论和解析理论的研究方法,推导出lgΓ(x)的Kummer-Fourier级数,并通过它来计算积分∫_0~1lgΓ(x)ζ(z,x)dx。其研究结果对于Γ函数性质的进一步探讨以及傅里叶级数用于有关Γ函数和赫尔维茨ζ函数积分估值的研究具有一定的推动作用。

The research methods of elementary number theory and analytic theory are adopted. We derive in this note Kummer-Fourier series for lgF （ x ） by which we evaluate the integral ∫0 1lgΓ（x）ζ（z,x）dx,The calculation results will have some roles in promoting to research what use the Fourier-series in Gamma Function and Hurwitz Functional integral.