I want to construct an entire function with one zero at $0$, and zeros at negative natural numbers with degree $n$ (multiplicity $n$ at $z = -n$ for $n \geq 1$).
Does $f(z) = z\displaystyle\prod_{n=1}^{\infty}(z+n)^{-n}$ work?
I want to construct an entire function with one zero at $0$, and zeros at negative natural numbers with degree $n$ (multiplicity $n$ at $z = -n$ for $n \geq 1$).
Does $f(z) = z\displaystyle\prod_{n=1}^{\infty}(z+n)^{-n}$ work?