I've tried without success to look this up, but: The graph of the gamma function for negative reals has a critical point — call it x_n — between every pair of adjacent integers {-n, -n+1}. See e.g. https://en.wikipedia.org/wiki/Gamma_function#/media/File:Gamma_plot.svg <https://en.wikipedia.org/wiki/Gamma_function#/media/File:Gamma_plot.svg>. It appears that the points (x_n, |gamma(x_n)|) lie on the graph of some nice convex function y = f(x). Is there in some sense a "nicest" convex f that works here? * * * Alternatively, it likewise appears that the graph of y = |gamma(x)| for negative x has one tangency in each interval (-n, -n+1) (n > 0) with the graph of some nice convex function y = g(x) that lies very close to the graph of y = f(x) hinted at above. Sort of an "envelope". Perhaps it's more natural to nail the function g ??? If so, is there a unique "nicest" g that works here? —Dan