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The Maxima on-line user's manual

Algebra Calculator

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Deftaylor Calculator

Deftaylor

Function: deftaylor (<f_1>(<x_1>), <expr_1>, ..., <f_n>(<x_n>), <expr_n>) For each function <f_i> of one variable <x_i>, deftaylor defines <expr_i> as the Taylor series about zero. <expr_i> is typically a polynomial in <x_i> or a summation; more general expressions are accepted by deftaylor without complaint.

deftaylor (f(x), cos(x)-cos(y) + sum(x^i/(2^i*i!^2), i, 4, inf));
taylor (exp (sqrt (f(x))), x, 0, 4);

powerseries (<f_i>(<x_i>), <x_i>, 0) returns the series defined by deftaylor.

deftaylor returns a list of the functions <f_1>, ..., <f_n>. deftaylor evaluates its arguments.

Example:

          (%i1) deftaylor (f(x), x^2 + sum(x^i/(2^i*i!^2), i, 4, inf));
          (%o1)                          [f]
          (%i2) powerseries (f(x), x, 0);
                                inf
                                ====      i1
                                \        x         2
          (%o2)                  >     -------- + x
                                /       i1    2
                                ====   2   i1!
                                i1 = 4
          (%i3) taylor (exp (sqrt (f(x))), x, 0, 4);
                                2         3          4
                               x    3073 x    12817 x
          (%o3)/T/     1 + x + -- + ------- + -------- + . . .
                               2     18432     307200

(%o1)                                true
(%i2) 

Deftaylor Example

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