A superadditive property of Hadamard's gamma function (Q1032513)

Hadamard introduced his gamma function in 1894 by \[ H(x)= {1\over\Gamma(1- x)}\cdot{d\over dx}\log\Biggl({\Gamma(1/2- x/2)\over \Gamma(1- x/2)}\Biggr), \] where \(\Gamma\) is the Euler gamma function. The author studies monotonicity, convexity and superadditive properties of this function. For example \(H\) is strictly increasing in \([3,\infty)\); strictly convex in \([1.6,\infty)\), and superadditive in \([a,\infty)\), where \(a\) is the single solution to \(H(2t)= 2H(t)\) in \(t\in[1.5,\infty)\). A comprehensive bibliography on gamma functions and their inequalities can be fund at \url{http://www.math.ubbcluj.ro/~jsandor/letolt/art42}.