# Documentation

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# `numeric`::`gtdata`

Weights and abscissae of Gauss-Tschebyscheff quadrature

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## Syntax

```numeric::gtdata(`n`)
```

## Description

`numeric::gtdata(n)` returns the weights and the abscissae of the Gauss-Tschebyscheff quadrature rule with n nodes.

The Gauss-Tschebyscheff quadrature rule produces the exact integral for all integrands of the form with polynomials p(x) through degree 2 n - 1.

The exact weights b = [b1, …, bn] and abscissae c = [c1, …, cn] are given by

.

## Environment Interactions

`numeric::gtdata` is not sensitive to the environment variable `DIGITS`.

The function uses `option remember`.

## Examples

### Example 1

The following call produces exact data for the quadrature rule with two nodes:

`numeric::gtdata(2)`

## Parameters

 `n` The number of nodes: a positive integer

## Return Values

List `[b,c]` is returned. The lists ```b = [b1, …, bn]``` and ```c = [c1, …, cn]``` are the exact weights and abscissae of the Gauss-Tschebyscheff quadrature rule, respectively.

## Algorithms

The numerical integrator `numeric::quadrature` calls `numeric::gtdata` to provide the data for Gauss-Tschebyscheff quadrature.