Generalized Bessel function in Wolfram Language

Questions
1

Hello community, I am a PhD student in strong laser field physics.

I work with the calculation of the differential cross-section and decay rate in the presence of the laser field. I program my calculation using Mathematica. In my calculation, I need the Bessel function. I recognize that the Ordinary Bessel function is defined in Mathematica: BesselJ[n,z]

But, I have a problem with the Generalized Bessel Functions which have two arguments. Are they defined in Mathematica or not?

I appreciate any help from you.

With my best regards.

2

Check the Details section, just above the Examples.

3

Hi Sander,

what can be found related to Generalized Bessel in the details section?

Robert

4

The definition for n and z :

Screenshot2022-02-15at18.25.47.png

Friedrich Bessel generalized the differential equation that Bernoulli looked at (the n basically).

5

Im am not an expert, but I think this is just the definition of the standard Bessel function of the first kind.

Jn[z].

There is only one (complex) variable/dimension z involved, n is just a parameter.

The generalized Version would deal with multiple variables/dimensions.

e.g. Jn[x,y]

Robert

6

Aaah, maybe! So it has 3 arguments, the author did not provide any example, reference, or anything. So not sure what he/she means.