Writing sinh(√(p² + k²)π) as a product of functions of p and k

[NeoDevin]

I'm trying to solve a problem in E&M, and I got an equation which depends on p and q, which I can solve provided I can write $sinh(\sqrt{p^2 + k^2} \pi)$ as a product of a function of p, with a function of k. If I can do that, I can solve the problem, but I don't know how to do that part (or if it's even possible). Any ideas?

 

[StatMechGuy]

I would try writing the Taylor expansion of sinh and see if that gets you anywhere. However, I don't think you can split it up like that...

 

[dextercioby]

Most likely it's a transcendental equation (since sinh is a transcendental function) that can't be solved analytically... Sad situation.

 

[Meir Achuz]

I think if you look at an earlier stge of the problem, you may be able to separate there.