论文标题
部分可观测时空混沌系统的无模型预测
An asymptotic approximation for the Riemann zeta function revisited
论文作者
论文摘要
我们重新访问用作者和S. CANG在方法应用中给出的标准化不完整的伽马函数表示的Riemann zeta函数$ζ$ζ$。肛门。 {\ bf 4}（1997）449--470。使用不完整的伽马功能的均匀渐近学在关键行上产生$ζ$ $ z $ s = 1/2+it $ as $ t \ to $ t \ to+\ histty $的渐近膨胀。主要术语涉及原始的dirichlet系列，该系列通过适当参数的互补误差函数以及一系列校正项平滑。在这里，目的是通过以$ω$的反逆权表示$ω^2 =πs/（2i）$，以更具用户友好的格式呈现这些校正项，乘以涉及参数$ω$的三角函数的系数。
We revisit a representation for the Riemann zeta function $ζ(s)$ expressed in terms of normalised incomplete gamma functions given by the author and S. Cang in Methods Appl. Anal. {\bf 4} (1997) 449--470. Use of the uniform asymptotics of the incomplete gamma function produces an asymptotic-like expansion for $ζ(s)$ on the critical line $s=1/2+it$ as $t\to+\infty$. The main term involves the original Dirichlet series smoothed by a complementary error function of appropriate argument together with a series of correction terms. It is the aim here to present these correction terms in a more user-friendly format by expressing then in inverse powers of $ω$, where $ω^2=πs/(2i)$, multiplied by coefficients involving trigonometric functions of argument $ω$.
