Let $\Gamma(s)$ be the Gamma function, extension of the factorial function to complex numbers.
My question is:
Fixed $y \in \mathbb{R_+}$ is it true that $\left| \Gamma(x+iy) \right|$, the modulus of gamma function, is strictly decreasing when $x \in (0,\frac{1}{2})$
Best Answer
False for $y=1$. Here is the graph of $|\Gamma(x+i)|$ for $0 < x < 1/2$.