• September 17th 2008, 08:05 AM
minivan15
[integral from 0 to pi/2] dx/SQRT(a - cosx)

(a >1)

I need to write this in terms of the elliptic integrals F

the elliptic integral of the first kind is F(k,q) = [integral from 0 to q]
$
du/SQRT(1 - (ksinu)^2)
$

I do not see a starting point on this! :(

I know elliptic integrals are tricky and ambiguous and all that...I merely need to REWRITE the given integral in terms of F

• September 17th 2008, 01:45 PM
shawsend
If $\int_{0}^{\pi/2}\frac{dx}{\sqrt{a-\cos(x)}}=\frac{2}{\sqrt{a-1}}\int_0^{\pi/4}\frac{du}{\sqrt{1-\frac{2}{a-1}\sin^2(u)}}$

can you use the identity $\sin^2(x/2)=\frac{1-\cos(x)}{2}$ to get there? Just make the substitution for $cos(x)$, and another one $u=x/2$.
• September 17th 2008, 10:01 PM
minivan15
I'm not sure. Sorry. Looks then to me $a$ needs to be greater than $3$.