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.(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Binomial Series

**Physics Forums | Science Articles, Homework Help, Discussion**