Nemes G
School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
Proc Math Phys Eng Sci. 2017 Jul;473(2203):20170363. doi: 10.1098/rspa.2017.0363. Epub 2017 Jul 5.
In this paper, we reconsider the large- asymptotic expansion of the Hurwitz zeta function (,). New representations for the remainder term of the asymptotic expansion are found and used to obtain sharp and realistic error bounds. Applications to the asymptotic expansions of the polygamma functions, the gamma function, the Barnes -function and the -derivative of the Hurwitz zeta function (,) are provided. A detailed discussion on the sharpness of our error bounds is also given.
在本文中，我们重新考虑了赫维茨zeta函数(\zeta(s,q))的大渐近展开。找到了渐近展开余项的新表示形式，并用于获得精确且实际的误差界。给出了其在多伽马函数、伽马函数、巴恩斯函数以及赫维茨zeta函数(\zeta(s,q))的(q)导数的渐近展开中的应用。还对我们误差界的精确性进行了详细讨论。
