for . Here, is an integral valued parameter known as the number of degrees of freedom. is a constant depending on . For to be a p.d.f., is must satisfy

Since is only defined for , it is sufficient for it to satisfy

Hence,

We substitute , so that , and

We notice that this is the Euler gamma function, defined by

with . Hence,

Therefore,

We can now make the definition

Alexander Frolkin 2001-02-01