  Several representations of the exact cdf of the sum of squares of n
independent gamma-distributed random variables Xi are given, in particular by a
series of gamma distribution functions. Using a characterization of the gamma
distribution by Laha, an expansion of the exact distribution of the sample
variance is derived by a Taylor series approach with the former distribution as
its leading term. In particular for integer orders alpha some further series
are provided, including a convex combination of gamma distributions for alpha =
1 and nearly of this type for alpha > 1. Furthermore, some representations of
the distribution of the angle Phi between (X1,...,Xn) and (1,...,1) are given
by orthogonal series. All these series are based on the same sequence of easily
computed moments of cos(Phi).
