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arXiv · 2508.05872

Uniform asymptotic expansions for generalised trigonometric integrals and their zeros

T. M. Dunster
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Abstract

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).

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T. M. Dunster. 2025-08-07. Uniform asymptotic expansions for generalised trigonometric integrals and their zeros. https://arxiv.org/abs/2508.05872

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