# Power series

1. Jan 25, 2006

### teng125

may i know how to solve this ques:find the power series representation for arctan (x)

i know that arctan (x) = integ 1/(1 + x^2) but then from here i don't know how to continue.
pls help......

2. Jan 25, 2006

### Hurkyl

Staff Emeritus
It seems to me if you're looking for the power series of the thing on the left hand side, then you might want to try looking for the power series of the thing on the right hand side.

3. Jan 26, 2006

### teng125

ya i'm looking for the thing on the left hand side.....pls help

4. Jan 26, 2006

### finchie_88

Take the thing on the right, and differentiate it a few times, and let x = 0 each time.

$$f(x) = f(0) + xf'(0) + \frac{x^2}{2!}f''(0) + ...$$

Where f'(0) represents the derivative at x = 0. f''(0) is the second derivative etc. This will give a power series, then you can integrate term by term for the inverse tan function.

5. Jan 26, 2006

### Hurkyl

Staff Emeritus
One doesn't need to know any calculus at all to find the power series for $1/(1+x^2)$.

I gave you a big hint -- have you not tried to do anything with it? :grumpy:

6. Jan 26, 2006

### HallsofIvy

Staff Emeritus
Go back and read Hurkyl's reply again!