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

 chebCoeff R Documentation

## Chebyshev Polynomials

### Description

Chebyshev Coefficients for Chebyshev polynomials of the first kind.

### Usage

``````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

``````##  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
``````

pracma documentation built on Nov. 10, 2023, 1:14 a.m.