I can't seem to prove this but I also cannot find a counter example. I am dealing with the idea of a function that is constant on the imaginary axis and is defined through an unbound domain. Is it a constant function?If so, why? And if it isn't, can you show me such function?
I would like to note that this is not a function with ImF being constant, but F is constant when fed imaginary numbers.
Thank aplenty.