The gamma function - an eclectic tour

Abstract: The gamma function originated 280 years ago with the work of Euler
and a little later Legendre. In 1812 Gauss, in his great memoir on the
hypergeometric series, studied this function as a function of a complex
variable, deducing its properties as by-products of his investigations on the
hypergeometric function. Forty seven years later the memoir of Riemann on the
distribution of primes appeared, in which one finds the famous functional
equation relating the gamma and the zeta functions. Moving to the twentieth
century, some of the results arising from a formula due to Ramanujan were
also discovered independently in 1916 by M. Riesz in connection with the Riemann
hypothesis. This talk focuses  on the history of the gamma  function and
shall conclude with some recent works, one of which is joint with P. Zvengrowski
and concerns the horizontal monotonocity of $|\Gamma (z)|$.