Open Collections

Description

This work arose out of joint work with Jonathan M. Borwein (1951--2016), undertaken while he was the Distinguished Visiting Scholar in Residence at Western (April-August 2016). That work was a survey of articles in the American Mathematical Monthly on the~$\Gamma$ function, of which there were nearly fifty. The survey identified some gaps: visualization, computation, and perhaps most surprisingly \textsl{nothing} on the functional inverse of~$\Gamma$, which we denote~$y=\invG(x)$ if~$x=\Gamma(y)$. This is multivalued with infinitely many branches. In this talk, I show that one can invert Stirling's original approximation (which is more accurate than the popular approximation by that name) to give a surprisingly accurate asymptotic formula for~$\invG$.