$\Delta y=e^{sy}$ or: How I Learned to Stop Worrying and Love the $\Gamma$-function

James David Nixon

For a nice holomorphic function $f(s,z)$ in two variables, a respective holomorphic Gamma function $\Gamma ={\Gamma }_f$ is constructed, such that $f(s,\Gamma (s))=\Gamma (s+1)$. Along the way, we fa…