What can we learn about the constants in the limit of k_3 for the E equation?

[Apteronotus]

Hi,

If
<br /> k_3 \cdot (A_1 \cos k_1 x + A_2 \sin k_1 x)\cdot(B_1 \cos k_2 y + B_2 \sin k_2 y)\cdot(C_1 e^{k_3 z}-C_2 e^{-k_3 z})=E<br />

in the limit as \sqrt{x^2+y^2+z^2}\rightarrow\infty

Can we infer anything about any of the constants?

 

[Stephen Tashi]

in the limit as \sqrt{x^2+y^2+z^2}\rightarrow\infty

One way to let \sqrt{x^2 + y^2 + z^2} approach infinity is to set y = 0, z= 0 and let x approach infinity. Do you really mean to allow that kind of approach? if so, won't the constants have to be chosen so the the expression is identically zero for all values of x ?