∞

f (n) (x

o

)

 

f (x) = ∑

 

 

⋅ (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,

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

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