On Quasi-Gamma Functions

We define the quasi-gamma functions as the functions

such that

f(1)=1 f ( 1 ) = 1

,

f(x+1)=xf(x) f ( x + 1 ) = x f ( x )

for every

x>0 x > 0

, and

f f

is quasi-convex. The main example of quasi-gamma function is the gamma function defined by Euler. We study some properties of the quasi-gamma functions and of the class

{\emph Q} Q

of these functions.