Thread: please if you know about elliptic integrals I NEED help!

[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]

PLEASE if you know anything about elliptic integrals I need your help!

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

thank you in advance for your help!

If

can you use the identity to get there? Just make the substitution for , and another one .

using your idea:

SQRT(a -(1 - 2(sinx/2)^2) = SQRT( a - 1 + 2(sinx/2)^2)

then factoring out a - 1 gives SQRT(a-1) * SQRT(1 + 2/(a-1)*(sinx/2)^2)

where k^2 is both negative and not necessarily less than one...the conditions for k in elliptic integrals are 0< k <1

did I do something wrong, or is the idea slightly off? I tried playing around with the concept but didn't get anywhere. Is there another answer or is this one correct but I'm just doing it incorrectly?

I'm not sure. Sorry. Looks then to me needs to be greater than .