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I'm looking for a function (preferrably in Python) which takes a complex number $a$ as input, and outputs the zeros of the function $f:x \rightarrow J_x(a)$ where $J_x(a)$ is the Bessel function of the first kind. This problem is relevant to solving a Schroedinger equation in a 1D condensed matter system (N.B. I am not asking to find the zeros of the bessel function $f:x \rightarrow J_n(x)$).

Does anybody know of a programming language such as Python, Wolfram language, etc. which has this built-in; and if so what is that function? It would save me the effort of implementing some sort of Newton's method-esque function myself.

Please let me know if this belongs on stackoverflow.

Poo2uhaha
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    You want all the zeros in the complex plane? I think there are typically infinitely many. Maple's fsolve will find solutions in a given rectangle. Unfortunately its RootFinding package seems not to work here because Maple doesn't know the derivative of $J(x,a)$ with respect to $x$. – Robert Israel Mar 29 '24 at 20:00
  • @RobertIsrael, yes, it's a tough question since I can't seem to get a hold of that derivative either... There must be some numerical result I can use somewhere though. All the best. – Poo2uhaha Mar 30 '24 at 10:15
  • There are derivatives here, but they may be a bit long – Тyma Gaidash Mar 30 '24 at 13:17

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