标题： 误差界对于渐近展开的Hartman-Watson积分 显示英文标题

标题： Error bound for the asymptotic expansion of the Hartman-Watson integral

摘要： 本文给出了Hartman-Watson分布的渐近展开式中首项误差的一个界，适用于$t\to 0$渐近展开式的$\theta(r,t)$情形，在$rt=\rho$常数区域内成立。 首项的形式为$\theta(\rho/t,t)=\frac{1}{2\pi t}e^{-\frac{1}{t} (F(\rho)-\pi^2/2)} G(\rho) (1 + \vartheta(t,\rho))$，其中误差项在$\rho$范围内被均匀界，当$|\vartheta(t,\rho)|\leq \frac{1}{70}t$成立时。 显示英文摘要

摘要： This note gives a bound on the error of the leading term of the $t\to 0$ asymptotic expansion of the Hartman-Watson distribution $\theta(r,t)$ in the regime $rt=\rho$ constant. The leading order term has the form $\theta(\rho/t,t)=\frac{1}{2\pi t}e^{-\frac{1}{t} (F(\rho)-\pi^2/2)} G(\rho) (1 + \vartheta(t,\rho))$, where the error term is bounded uniformly over $\rho$ as $|\vartheta(t,\rho)|\leq \frac{1}{70}t$.