# Thread: Formula for power series

1. ## Formula for power series

Which is a general form of formula for developing this kind of function $\displaystyle (1+x)^a$ (a is some number) into power series?

2. ## Re: Formula for power series

Originally Posted by Garas
Which is a general form of formula for developing this kind of function $\displaystyle (1+x)^a$ (a is some number) into power series?
Some?!

3. ## Re: Formula for power series

OK, let's say that a belongs to Q, it's not really important i just need a formula.

4. ## Re: Formula for power series

for example if you want to develop this function 1/sqrt{1+x} you use that formula, so it's very applicable for any function that you can transform into $\displaystyle (1+x)^a$ like arcsinx,ln(x+sqrt{1+x}) and similar.

5. ## Re: Formula for power series

Originally Posted by Garas
Which is a general form of formula for developing this kind of function $\displaystyle (1+x)^a$ (a is some number) into power series?
Is...

$\displaystyle (1+x)^{a}= 1 + a x + \frac{a (a-1)}{2} x^{2} + \frac{a (a-1) (a-2)}{6} x^{3} + ... + \frac{a (a-1) ...(a-n+1)}{n!} x^{n} + ...$ (1)

... and (1) is valid for any real or complex a...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

6. ## Re: Formula for power series

Originally Posted by Garas
Which is a general form of formula for developing this kind of function $\displaystyle (1+x)^a$ (a is some number) into power series?
You should look up Newton's Generalised Binomial Theorem.