How to numerically calculate the function 1/(x^2 - alpha^2) with GSL routines?

[emilroz]

Hi, already tried few routines from GSL and it seems it doesn't work.

Function: 1/(x^2 - alpha^2)

Can anyone tell how to calculate that numerically.
Tried to do it by "hand" as well but no good results.

Cheers.

 

[Defennder]

You don't need a numerical solution for this. I assume alpha is just an arbitrary constant. Note that the denominator can be written as a product of 2 functions.

 

[emilroz]

Thanks for respond.

Actually the problem is bit more complicated. Integral is (-inf, inf) and whole function is equal to:

f(y,z) = int_(-inf,inf) dx [2y/(x^2-y^2) ] * [ 1/(exp{x-z} +1)]

What do u think about that.

 

[Defennder]

You mean this:
$$f(x,y,z) = \int^{\infty}_{-\infty} \left( \frac{2y}{x^2-y^2} \right) \frac{dx}{e^{x-z}+1}$$

 

[emilroz]

Exactly