论文标题
与Hurwitz Zeta功能有关的广义超几何扩展
Generalized hypergeometric expansion related to the Hurwitz zeta function
论文作者
论文摘要
当由仿射复合物图组成时，我们研究了分数部分和相关的对数函数的不完整的梅林转化。我们以两种不同的方式评估相应的积分，这些积分在两侧的超几何函数中产生相等性。这些平等性捕获了Hurwitz Zeta的基本分析特性，例如Meromormormormormormormormormormormormormormormormormormorormormormormorormormormorormormormormorormortemation和功能方程。我们给出参与系列的收敛速度。作为一种特殊情况，我们发现，对日志 - sine对假想成分中分数的变形的收敛速率被延续到这些平等性。
We study the incomplete Mellin transformation of the fractional part and the related log-sine function when composed by an affine complex map. We evaluate the corresponding integral in two different ways which yields equalities with series in hypergeometric functions on each side. These equalities capture basic analytic properties of the Hurwitz zeta function like meromorphic extension and the functional equation. We give rates of convergence for the involved series. As a special case we find that the exponential rate of convergence for the deformation of the log-sine to the fractional part in the imaginary component is carried over to these equalities.
