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 a Taylor series, and the order of the series to be produced. Function SERIES returns two output items a list with four items, and an expression for h = x - a, if the second argument in the function call is ‘x=a’, i.e., an expression for the increment h. The list returned as the first output object includes the following items:

1 - Bi-directional limit of the function at point of expansion, i.e., lim f (x)

x→a

2 - An equivalent value of the function near x = a 3 - Expression for the Taylor polynomial

4 - Order of the residual or remainder

Because of the relatively large amount of output, this function is easier to handle in RPN mode. For example, the following screen shots show the RPN stack before and after using function SERIES:

Drop the contents of stack level 1 by pressing ƒ, and then enter µ, to decompose the list. The results are as follows:

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