### The Maxima on-line user's manual

Algebra 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.

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)

### Related Examples

##### deftaylor-float-integrate-powerseries-sum

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##### deftaylor-float-integrate-powerseries-sum

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##### deftaylor-exp-inf-sqrt-sum

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##### deftaylor-sum

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##### deftaylor-inf-powerseries-sum

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##### deftaylor-exp-inf-powerseries-sqrt-sum

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##### deftaylor-inf-sum

deftaylor (f(x), x^2 ...

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##### deftaylor-inf-sum

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