# ball_integrals

ball_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

The interior of the unit ball in 3D is defined by

```        x^2 + y^2 + z^2 <= 1
```

The integrands are all of the form

```        f(x,y,z) = x^e1 * y^e2 * z^e3
```
where the exponents 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.

### Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

### Languages:

ball_integrals is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

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triangle_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2d.

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### Reference:

1. Gerald Folland,
How to Integrate a Polynomial Over a Sphere,
American Mathematical Monthly,
Volume 108, Number 5, May 2001, pages 446-448.

### Source Code:

Last revised on 17 January 2020.