taylor {calculus}  R Documentation 
Computes the Taylor series of functions
or characters
.
taylor( f, var, params = list(), order = 1, accuracy = 4, stepsize = NULL, zero = 1e07 )
f 

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 
params 

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. 
list
with components:
the Taylor series.
the approximation order.
data.frame
containing the variables, coefficients and degrees of each term in the Taylor series.
Guidotti, E. (2020). "calculus: High dimensional numerical and symbolic calculus in R". https://arxiv.org/abs/2101.00086
Other polynomials:
hermite()
Other derivatives:
derivative()
### univariate taylor series (in x=0) taylor("exp(x)", var = "x", order = 2) ### univariate taylor series of userdefined 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*(y1)", var = c(x=0, y=1), order = 4) ### multivariate taylor series of userdefined functions (in x=0 and y=1) f < function(x,y) x*(y1) 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)