defrule SciMax Toolbox del

SciMax Toolbox >> deftaylor

deftaylor

Maxima Function

Calling Sequence

deftaylor (f_1(x_1), expr_1, ..., f_n(x_n), expr_n)

Description

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.

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
defrule SciMax Toolbox del