Solving E&M Problem: Need Help Writing sinh(...) as a Product of p & k

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Homework Help Overview

The discussion revolves around a problem in electromagnetism (E&M) that involves manipulating the hyperbolic sine function, specifically expressing sinh(√(p² + k²) π) as a product of functions of p and k. The original poster is seeking assistance with this transformation to progress in solving their equation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants suggest various approaches, including the use of Taylor expansion to explore the properties of the sinh function. There is also speculation about the nature of the equation, with some questioning the feasibility of separating the variables as desired.

Discussion Status

The discussion is ongoing, with participants exploring different lines of reasoning and approaches. Some guidance has been offered regarding potential methods, but there is no consensus on the possibility of achieving the desired separation of functions.

Contextual Notes

Participants note the complexity of the problem, particularly the transcendental nature of the sinh function, which may limit analytical solutions. There is an acknowledgment of the need to consider earlier stages of the problem for potential separation.

NeoDevin
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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 [itex]sinh(\sqrt{p^2 + k^2} \pi)[/itex] 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?
 
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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...
 
Most likely it's a transcendental equation (since sinh is a transcendental function) that can't be solved analytically... Sad situation.
 
I think if you look at an earlier stge of the problem, you may be able to separate there.
 

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