Which is a general form of formula for developing this kind of function $\displaystyle (1+x)^a$ (a is some number) into power series?
Follow Math Help Forum on Facebook and Google+
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?!
OK, let's say that a belongs to Q, it's not really important i just need a formula.
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.
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 $\displaystyle \chi$ $\displaystyle \sigma$
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.