Let's make another function that equals its own derivative. I'm very curious as to why this is happening!
\( g(s) = \sum_{n=-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-(y+n)^2} \frac{s^y}{\Gamma(y+1)}dy \)
Differentiate and watch for your self!
Does this mean the function cannot converge? I know the integral converges, not sure about the summation though.
Using the other method I can easily create a function that converges for some domain... What's going on?
\( g(s) = \sum_{n=-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-(y+n)^2} \frac{s^y}{\Gamma(y+1)}dy \)
Differentiate and watch for your self!
Does this mean the function cannot converge? I know the integral converges, not sure about the summation though.
Using the other method I can easily create a function that converges for some domain... What's going on?