Binomial Series

  • Thread starter Oxymoron
  • Start date
870
0
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!
 

HallsofIvy

Science Advisor
Homework Helper
41,731
884
What kind of help do you want? Do you have any reason to believe that what you have is not correct?
 
870
0
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).

Thanks.
 

Related Threads for: Binomial Series

  • Last Post
Replies
6
Views
810
  • Last Post
Replies
4
Views
654
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
7
Views
4K
  • Last Post
Replies
3
Views
821
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
6
Views
8K

Hot Threads

Top