# chebCoeff: Chebyshev Polynomials In pracma: Practical Numerical Math Functions

## Description

Chebyshev Coefficients for Chebyshev polynomials of the first kind.

## Usage

 `1` ```chebCoeff(fun, a, b, n) ```

## Arguments

 `fun` function to be approximated. `a, b` endpoints of the interval. `n` an integer `>= 0`.

## Details

For a function `fun` on on the interval `[a, b]` determines the coefficients of the Chebyshev polynomials up to degree `n` that will approximate the function (in L2 norm).

## Value

Vector of coefficients for the Chebyshev polynomials, from low to high degrees (see the example).

## Note

See the “Chebfun Project” <https://www.chebfun.org/> by Nick Trefethen.

## References

Weisstein, Eric W. “Chebyshev Polynomial of the First Kind." From MathWorld — A Wolfram Web Resource. https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html

`chebPoly`, `chebApprox`

## Examples

 ```1 2 3 4 5 6 7 8``` ```## Chebyshev coefficients for x^2 + 1 n <- 4 f2 <- function(x) x^2 + 1 cC <- chebCoeff(f2, -1, 1, n) # 3.0 0 0.5 0 0 cC[1] <- cC[1]/2 # correcting the absolute Chebyshev term # i.e. 1.5*T_0 + 0.5*T_2 cP <- chebPoly(n) # summing up the polynomial coefficients p <- cC %*% cP # 0 0 1 0 1 ```

### Example output

```
```

pracma documentation built on Dec. 11, 2021, 9:57 a.m.