
Infinite series
A function f(x) can be expanded into an infinite series around a point x=x0 by using a Taylor’s series, namely,
∞ | ( n) |
|
|
| |
f ( x) = ∑ | f |
| ( xo ) | ⋅ ( x − xo ) n |
|
|
|
|
| ||
n=0 | n! | , | |||
|
|
|
|
|
where f(n)(x) represents the
If the value x0 = 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
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
Function SERIES produces a Taylor polynomial using as arguments the function f(x) to be expanded, a variable name alone (for Maclaurin’s
Page