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Math Help - Formula for power series

  1. #1
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    Formula for power series

    Which is a general form of formula for developing this kind of function (1+x)^a (a is some number) into power series?
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    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Formula for power series

    Quote Originally Posted by Garas View Post
    Which is a general form of formula for developing this kind of function (1+x)^a (a is some number) into power series?
    Some?!
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  3. #3
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    Re: Formula for power series

    OK, let's say that a belongs to Q, it's not really important i just need a formula.
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    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 (1+x)^a like arcsinx,ln(x+sqrt{1+x}) and similar.
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    MHF Contributor chisigma's Avatar
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    Re: Formula for power series

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

    (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

    \chi \sigma
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  6. #6
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    Re: Formula for power series

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