Given a standard n-1 simplex
is a positive integer, and a vector
I need to evaluate the integral
are real non-negative numbers, and m
is an integer between 1 and n
The integral is taken over the standard n
with respect to
Similar integrals that have well-known solutions are:
is the Gamma function.
Note that the only difference between (1) and (3) is that the second sum in (3) goes from m
+1 to n
instead of from m
. This difference is however important, surely making the solution to (1) more complicated than that of (3).