Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Error bounds for a uniform asymptotic approximation of the zeros of the Bessel function $J_ν(x)$ (2405.08208v5)

Published 13 May 2024 in math.CA

Abstract: A recent asymptotic expansion for the positive zeros $x=j_{\nu,m}$ ($m=1,2,3,\ldots$) of the Bessel function of the first kind $J_{\nu}(x)$ is studied, where the order $\nu$ is positive. Unlike previous well-known expansions in the literature, this is uniformly valid for one or both $m$ and $\nu$ unbounded, namely $m=1,2,3,\ldots$ and $1 \leq \nu < \infty$. Explicit and simple lower and upper error bounds are derived for the difference between $j_{\nu,m}$ and the first three terms of the expansion. The bounds are sharp in the sense they are close to the value of the fourth term of the expansion (i.e. the first neglected term).

Summary

We haven't generated a summary for this paper yet.

X Twitter Logo Streamline Icon: https://streamlinehq.com