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Full Version: Look-alike functions.
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Consider the argument of An entire function within a unit radius.

If they are identical for 2 distinct entire function with that radius we call them " look-alike ".

For instance 2sinh(z+3) and exp(z+3) are look-alikes.

You might have noticed that all look-alikes to the above satisfy

F ' ' (z) = F(z).

So yes this relates to differential equations.

I think cauchy-riemann matters.

This is probably isomorphic to something well understood.


sinh(t) is defined in terms of exp(t). Why is it notable that they are similar sometimes?