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Zeros of Bessel functions of the first kind $J_\alpha$

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Numbers

$\alpha$

$n$

$n$^{th} root of $J_\alpha$

INPUT{numbers.yaml} (not shown in preview)

Definition

The list contains the first positive zeros of Bessel functions of the first kind $J_\alpha$.

Parameters

$\alpha$

— complex number

$n$

— integer ($n \geq 1$)

Formulas

(1)

The $n$'th root of $J_{1/2}(x)$ equals $n\pi$.

Comments

(2)

This table currently restricts to the important special case $\alpha \in \frac{1}{2}\mathbb{Z}_{\geq 0}$.

Links

[1]

mpmath (Python library)

Data properties