(notes by Roberto Bigoni)
The integrals that express the Euler's Gamma function
are such that
In particular, if x is a natural number greater than 1, we have
In general
To calculate the value of Gamma when its argument is an half-integral number, we must first calculate
Using the variable substitution t=z2 we get
This integral is a
gaussian integral
and its value is
.
So
The values of Gamma for the following half-integral arguments can be obtained recursively
