# disk_integrals

disk_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of a disk of radius R centered at the origin in 2D.

The interior of the disk is defined by

```        x^2 + y^2 <= r^2
```

The integrands are all of the form

```        f(x,y) = x^e1 * y^e2
```
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.

### Languages:

disk_integrals is available in a MATLAB version and an Octave version and a Python version.

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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 05 November 2022.