Add Modified Bessel Function

[fhumeau]

As there is a BesselJ function, it would be interesting to implement the Modified Bessel function or BesselI.
Here is the reference for the Modified Bessel Function of the First Kind.

Thanks,
Florian

[axkr]

I' ve ported these Bessel and Hypergeometric functions:

• https://github.com/axkr/symja_android_library/blob/master/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/builtin/functions/BesselJS.java
• https://github.com/axkr/symja_android_library/blob/master/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/builtin/functions/HypergeometricJS.java

from the math.js JavaScript library:

• https://github.com/paulmasson/math/blob/master/src/functions/bessel.js
• https://github.com/paulmasson/math/blob/master/src/functions/hypergeometric.js

Maybe someone is interested to port these functions to hipparchus in a better "Java" style?

The org.hipparchus.complex.Complex class is already used in these functions.

As far as I know the "MIT license" from math.js should be compatible with the "Apache" license used by hipparchus.

[maisonobe]

Yes MIT licence is compatible.
I'll look at this, but probably not right now, as I have other tasks to finish first.

[VincentCucchietti]

Yes MIT licence is compatible. I'll look at this, but probably not right now, as I have other tasks to finish first.

Hi @maisonobe, someone in the CS team is going to do it as it is necessary for the internship subject of @fhumeau.

Cheers,
Vincent

[maisonobe]

Great, thanks for doing it!

[Serrof]

@fhumeau @VincentCucchietti has it been implemented indeed and if yes can it be contributed here?
Cheers.

[VincentCucchietti]

It must have been implemented locally, @fhumeau should know better than me.
Cheers

[MaximeJo]

Hello,

Sorry this is an old thread and I missed the discussions.

@fhumeau ended up only developing asymptotic series expansion for the modified Bessel functions of order 0 (and maybe 1) since the numbers he had to deal with were very large.

So I guess this point is still opened...