taylor {calculus} R Documentation

## Taylor Series Expansion

### Description

Computes the Taylor series of `functions` or `characters`.

### Usage

```taylor(
f,
var,
params = list(),
order = 1,
accuracy = 4,
stepsize = NULL,
zero = 1e-07
)
```

### Arguments

 `f` `character`, or `function` returning a `numeric` scalar value. `var` vector giving the variable names with respect to which the derivatives are to be computed and/or the point where the derivatives are to be evaluated (the center of the Taylor series). See `derivative`. `params` `list` of additional parameters passed to `f`. `order` the order of the Taylor approximation. `accuracy` degree of accuracy for numerical derivatives. `stepsize` finite differences stepsize for numerical derivatives. It is based on the precision of the machine by default. `zero` tolerance used for deciding which derivatives are zero. Absolute values less than this number are set to zero.

### Value

`list` with components:

f

the Taylor series.

order

the approximation order.

terms

`data.frame` containing the variables, coefficients and degrees of each term in the Taylor series.

### References

Guidotti, E. (2020). "calculus: High dimensional numerical and symbolic calculus in R". https://arxiv.org/abs/2101.00086

Other polynomials: `hermite()`

Other derivatives: `derivative()`

### Examples

```### univariate taylor series (in x=0)
taylor("exp(x)", var = "x", order = 2)

### univariate taylor series of user-defined functions (in x=0)
f <- function(x) exp(x)
taylor(f = f, var = c(x=0), order = 2)

### multivariate taylor series (in x=0 and y=1)
taylor("x*(y-1)", var = c(x=0, y=1), order = 4)

### multivariate taylor series of user-defined functions (in x=0 and y=1)
f <- function(x,y) x*(y-1)
taylor(f, var = c(x=0, y=1), order = 4)

### vectorized interface
f <- function(x) prod(x)
taylor(f, var = c(0,0,0), order = 3)

```

[Package calculus version 0.3.1 Index]