论文标题
第一种修改的贝塞尔功能的积分的界限，涉及它的表达式
Bounds for an integral of the modified Bessel function of the first kind and expressions involving it
论文作者
论文摘要
对于积分$ \ int_0^x \ mathrm {e}^{ - γt} t^νi_ν（t）\，\ Mathrm {d} t $，$ x> 0 $，$ x> 0 $，$ c {1} {1} {2} $ 0 <γ<1 $，获得了简单的上限和下限。我们对此积分的大多数界限都紧密地为$ x \ rightarrow \ infty $。我们将我们的一种不平等应用之一绑定到涉及该积分的一些表达式。其中两个表达式出现在Stein的方差近似方法中，我们的界限将允许对方法进行技术进步。
Simple upper and lower bounds are obtained for the integral $\int_0^x\mathrm{e}^{-γt}t^νI_ν(t)\,\mathrm{d}t$, $x>0$, $ν>-\frac{1}{2}$, $0<γ<1$. Most of our bounds for this integral are tight as $x\rightarrow\infty$. We apply one of our inequalities to bound some expressions involving this integral. Two of these expressions appear in Stein's method for variance-gamma approximation, and our bounds will allow for a technical advancement to be made to the method.
