Uniform asymptotic expansions for generalised trigonometric integrals and their zeros

2025/08/07 by Dunster, T. M.
#33B15 #33E20 #34E05 #34E20 #34M60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.05872

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).

Citations

• Uniform asymptotic expansions for Bessel functions of imaginary order and their zeros
• Uniform asymptotic expansions for the zeros of Bessel functions
• Liouville-Green expansions of exponential form, with an application to modified Bessel functions

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