R: Taylor Series Approximation

taylor {pracma} | R Documentation

## Taylor Series Approximation

### Description

Local polynomial approximation through Taylor series.

### Usage

    taylor(f, x0, n = 4, ...)

### Arguments

`f` | differentiable function.
`x0` | point where the series expansion will take place.
`n` | Taylor series order to be used; should be `n <= 4`.
`...` | more variables to be passed to function `f`.

### Details

Calculates the first four coefficients of the Taylor series through numerical differentiation and uses some polynomial ‘yoga’.

### Value

Vector of length `n+1` representing a polynomial of degree `n`.

### Note

TODO: Pade approximation.

### See Also

`fderiv`

### Examples

    taylor(sin, 0, 4)  #=> -0.1666666  0.0000000  1.0000000  0.0000000
    taylor(exp, 1, 4)  #=>  0.04166657 0.16666673 0.50000000 1.00000000 1.00000000

    f <- function(x) log(1+x)
    p <- taylor(f, 0, 4)
    p                     # log(1+x) = 0 + x - 1/2 x^2 + 1/3 x^3 - 1/4 x^4 +- ...
                          # [1] -0.250004  0.333334 -0.500000  1.000000  0.000000

    ## Not run:
    x <- seq(-1.0, 1.0, length.out=100)
    yf <- f(x)
    yp <- polyval(p, x)
    plot(x, yf, type = "l", col = "gray", lwd = 3)
    lines(x, yp, col = "red")
    grid()
    ## End(Not run)

[Package pracma version 2.0.4 Index]