# chebyshev1_rule

chebyshev1_rule, a Python code which generates a specific Gauss-Chebyshev type 1 quadrature rule, based on user input.

The rule is written to three files for easy use as input to other programs.

The Gauss Chevbyshev type 1 quadrature rule is used as follows:

```        Integral ( A <= x <= B ) f(x) / sqrt ( ( x - A ) * ( B - x ) ) dx
```
is to be approximated by
```        Sum ( 1 <= i <= order ) w(i) * f(x(i))
```

### Usage:

chebyshev1_rule ( order, a, b, 'filename' )
where
• order is the number of points in the quadrature rule.
• a is the left endpoint;
• b is the right endpoint.
• filename specifies the output files: filename_w.txt, filename_x.txt, and filename_r.txt, containing the weights, abscissas, and interval limits.

### Languages:

chebyshev1_rule is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

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