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arXiv · 2504.04992

Error bound for the asymptotic expansion of the Hartman-Watson integral

Dan Pirjol
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Abstract

This note gives a bound on the error of the leading term of the $t\to 0$ asymptotic expansion of the Hartman-Watson distribution $\theta(r,t)$ in the regime $rt=\rho$ constant. The leading order term has the form $\theta(\rho/t,t)=\frac{1}{2\pi t}e^{-\frac{1}{t} (F(\rho)-\pi^2/2)} G(\rho) (1 + \vartheta(t,\rho))$, where the error term is bounded uniformly over $\rho$ as $|\vartheta(t,\rho)|\leq \frac{1}{70}t$.

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Dan Pirjol. 2025-04-07. Error bound for the asymptotic expansion of the Hartman-Watson integral. https://arxiv.org/abs/2504.04992

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