Bounding the Gap Between Zeros of the Variable- Parameter Confluent Hypergeometric Function

Steven Langel

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arXiv · 2604.04840

Bounding the Gap Between Zeros of the Variable- Parameter Confluent Hypergeometric Function

Steven Langel

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Abstract

This paper derives a lower bound on the spacing between adjacent zeros of the confluent hypergeometric function $\Phi(a,b,z)$ when $a$ is variable and $(b,z) \in \mathbb{R}^+$ are known and fixed. Monotonicity of the bound is established, and the results are used to assess the accuracy of asymptotic approximations for the first passage probability of a Wiener process.

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Steven Langel. 2026-04-06. Bounding the Gap Between Zeros of the Variable- Parameter Confluent Hypergeometric Function. https://arxiv.org/abs/2604.04840

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