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Page 11-5

Infinite series

A function f(x) can be expanded into an infinite series around a point x=x

using a Taylor’s series, namely,

∑

∞

−⋅=

)(

xf ,

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, 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,

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HP 48gII Manuale Utente Pagina 140