Associated Laguerre Polynomial

[khauna]

Hello,
(quick backgroun info) : I am a physics student who has gone through pre quantum type material and a little of quantum mechanics. I am working in a lab with fortan code based on Quantum field theory.

Anyway I am working to change some pieces of this code to attempt to solve a problem by a different way. What I would like to know is:

Does anyone know if its possible to solve the Associated Laguerre Polynomials with fractional order? Normally you must use integers which we have done in our fortran coding. I need to change that but I want to know if using fractional order is possible with laguerre polynomials and will those solutions return real numbers?

Thanks for any help and let me know if I need to be more clear or provide more information,

~ Justin

 

[Dr Transport]

I suspect that you should be able to write the equation in a form that is either a Hypergeometric or Confluent Hypergeometric equation, then you can have fractional orders.

 

[khauna]

hmm i will look into this.

Thanks :)
~ Justin

 

[diggy]

I'd listen to Dr Transport over me, but I believe the AL polynomials are specific solutions for the more general Legendre function (when l,n are integers). You might be safer to revert back to that general solution. If your z is within a certain range, the Legendre function can be expressed by "Laplace's first integral", which doesn't deal with contour integration. If neither of those yield fruit, this is one I'm pretty positive I've seen solved numerically for arbitrary real numbers.

 

[khauna]

Yea I see what your getting at. I'll be sure to look into that also.

Thanks,
~ Justin