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Uniform asymptotic expansions for generalised trigonometric integrals and their zeros (2508.05872v1)
Published 7 Aug 2025 in math.CA
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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