hypersphere_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.
The surface of the unit hypersphere in M dimensions is defined by
sum ( 1 <= i <= m ) x(i)^2 = 1
The integrands are all of the form
f(x) = product ( 1 <= m <= m ) x(i) ^ e(i)where the exponents e are nonnegative integers. If any exponent is an odd integer, the integral will be zero. Thus, the "interesting" results occur when all exponents are even.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
hypersphere_integrals is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
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