taylor function

Taylor Series Expansion

Computes the Taylor series of functions or characters.

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.

Returns

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.

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)

References

Guidotti E (2022). "calculus: High-Dimensional Numerical and Symbolic Calculus in R." Journal of Statistical Software, 104(5), 1-37. tools:::Rd_expr_doi("10.18637/jss.v104.i05")

See Also

Other polynomials: hermite()

Other derivatives: derivative()