— preview —

Local extrema of Bessel functions of the first kind $J_\alpha$

edit on github
Numbers

$\alpha$

$n$

$n$^{th} local extremum of $J_\alpha$

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

Definition

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

Parameters

$\alpha$

— complex number

$n$

— integer ($n \geq 1$)

Comments

(1)

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

(2)

Note that we list $x=0$ for $\alpha=0$ as $J_0'(0)=0$ and for consistency with (3).

(3)

Local maxima arise for odd $n$, local minima for even $n$.

Links

[1]

mpmath (Python library)

Data properties