HP 48gII (xo ), f (x) = ∑, ⋅ (x − xo ) n, Infinite series, Functions TAYLR, TAYLR0, and SERIES, If the value x0 = 0, the series is referred to as a Maclaurin’s series

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)	(xo )
f (x) = ∑	f			⋅ (x − xo ) n	,
		n!
n=0

where f(n)(x) represents the n-th derivative of f(x) with respect to x, f(0)(x) = f(x).

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 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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