# Infinite Series; Functions Taylr, Taylr0, And Series - HP 48gII User Manual

Graphing calculator.

## Infinite series

A function f(x) can be expanded into an infinite series around a point x=x
using a Taylor's series, namely,
f
(n)
where f
(x) represents the n-th derivative of f(x) with respect to x, f
If the value x
= 0, the series is referred to as a Maclaurin's series.
0

### 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,
(
n
)
f
(
x
)
=
o
(
x
)
(
x
n
!
=
n
0
n
x
)
,
o
(0)
(x) = f(x).
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