HP 49g+ - Manual (Page 140)

Page 11-5
∑
∞
=
− ⋅ =
0
) (
) (
!
) (
) (
n
n
o
o
n
x x
n
x f
x f ,
where f (n) (x) represents the n-th derivative of f(x) with respect to x, f (0) (x) = f(x).
If the value x
0
= 0, the series is referred to as a Maclaurin’s series.
Functions TAYLR, TAYLR0, and SERIES
Functions TAYLR, TAYLR0, and SERIES are used to generate Taylor
polynomials, as well as Taylor series with residuals. These functions are
available in the CALC/LIMITS&SERIES menu described earlier in this Chapter.
Function TAYLOR0 performs a Maclaurin series expansion, i.e., about X = 0,
of an expression in the default independent variable, VX (typically ‘X’). The
expansion uses a 4-th order relative power, i.e., the difference between the
highest and lowest power in the expansion is 4. For example,
Function TAYLR produces a Taylor series expansion of a function of any
variable x about a point x = a for the order k specified by the user. Thus, the
function has the format TAYLR(f(x-a),x,k). For example,
Function SERIES produces a Taylor polynomial using as arguments the function
f(x) to be expanded, a variable name alone (for Maclaurin’s series) or an
expression of the form ‘variable = value’ indicating the point of expansion of