标题： 一般三角积分及其零点的均匀渐近展开 显示英文标题

标题： Uniform asymptotic expansions for generalised trigonometric integrals and their zeros

摘要： 对于广义三角积分的渐近展开式是用初等函数表示的，这些展开式适用于参数$a$的大值以及自变量的无界复数值。 这些展开式来自于不完全伽马函数的新Liouville-Green渐近展开式。 然后为广义三角积分的实零点构造了大$a$的渐近展开式，这些展开式在自变量大小（小或大）没有任何限制的情况下都是一致有效的。 显示英文摘要

摘要： Asymptotic expansions for generalised trigonometric integrals are obtained in terms of elementary functions, which are valid for large values of the parameter $a$ and unbounded complex values of the argument. These follow from new Liouville-Green asymptotic expansions for incomplete gamma functions. Asymptotic expansions for the real zeros of the generalised trigonometric integrals are then constructed for large $a$ which are uniformly valid without restriction on their size (small or large).