I am studying the special functions, including the Riemann Xi and Zeta, and everywhere a function $\pi^{-\frac x\pi}$ pops up, usually as multiplier to the Gamma function. But yet I am not sure this function has any significance outside Zeta function studies.
I wonder what other interesting properties the exponent with the base $\frac {1}{\sqrt[\pi]{\pi}}$ can possess. Does it appear anywhere else?