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Binomial Series

  1. Aug 29, 2003 #1
    I have been doing some questions on Binomial Series expansion and have been stuck on this particular question for a long time and desperately need some guidance.

    Q) Expand (1/(sqrt(1-b^2(sin^2)x)))), where b = sin(1/2(theta)) as a binomial series.

    Here is what I have done so far...

    Let x = (b^2(sin^2)x) because I want the expression in binomial form.

    So it becomes 1/sqrt(1 - x) with k = -1/2

    (1-x)^-1/2 can be written in binomial form... (S is capital sigma)

    = S(-1/2 n)(-x)^n
    = 1 + (-1/2)(-x) + ((-1/2)(-3/2)/2!)*(-x)^2 + ...
    = 1 + 1/2x - 3/8x^2 + ...
    = 1 + 1/2k^2sin^2x - 3/8k^4sin^4x + ...

    Any help on this question would be excellent!
  2. jcsd
  3. Aug 30, 2003 #2


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    What kind of help do you want? Do you have any reason to believe that what you have is not correct?
  4. Aug 31, 2003 #3
    Sorry about that. What I meant was that if my working was incorrect could someone correct me or offer a simpler way to do it (if any).

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