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

Abstract

This paper derives a lower bound on the spacing between adjacent zeros of the confluent hypergeometric function $\hat{I}¦(a,b,z)$ 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.