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

Algebra 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

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)

### Related Examples

##### powerseries

f(x)= (1/(1-x)^20);

g(x)= (1/(1-x)^5);

a(n) = Taylor(f(x)*g(...

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##### powerseries

powerseries ((1-((2^(...

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##### powerseries

powerseries(-2/(z-1),...

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##### powerseries

powerseries(1/x,x,0);

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##### powerseries-true-verbose

verbose: true;

powerseries((1/x),x,0);

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##### powerseries

powerseries((1-t)*(1-...

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##### powerseries

powerseries((1-3*z)/(...

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##### powerseries-true-verbose

verbose: true;

powerseries (ln(16+x...

Calculate

##### powerseries-sin

powerseries((x+1)^sin...

Calculate

##### powerseries

powerseries(1/ln(1+e^...

Calculate