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The Maxima on-line user's manual

Algebra Calculator

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Powerseries Calculator

Powerseries

Function: powerseries (<expr>, <x>, <a>) Returns the general form of the power series expansion for <expr> in the variable <x> about the point <a> (which may be inf for infinity): inf ==== \ n > b (x - a) / n ==== n = 0

niceindices(powerseries(%e^x, x, 0));
taylor(%e^x, x, 0, 6);
plot2d([trunc(taylor(%e^x, x, 0, 6)), %e^x], [x,-5,5]);

If powerseries is unable to expand <expr>, taylor may give the first several terms of the series.

When verbose is true, powerseries prints progress messages.

          (%i1) verbose: true$
          (%i2) powerseries (log(sin(x)/x), x, 0);
          cant expand
                                           log(sin(x))
          so well try again after applying the rule:
                                                  d
                                                / -- (sin(x))
                                                [ dx
                                  log(sin(x)) = i ----------- dx
                                                ]   sin(x)
                                                /
          in the first simplification we have returned:
                                       /
                                       [
                                       i cot(x) dx - log(x)
                                       ]
                                       /
                              inf
                              ====        i1  2 i1             2 i1
                              \      (- 1)   2     bern(2 i1) x
                               >     ------------------------------
                              /                i1 (2 i1)!
                              ====
                              i1 = 1
          (%o2)                -------------------------------------
                                                2

(%o1)                                true
(%i2) 

Powerseries Example

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