If
can you use the identity to get there? Just make the substitution for , and another one .
[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!
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 don understand about the reversal of polarity statement.I am new to elliptic integrals,i do have one doubt.whether i can get a variable solution when i use elliptical integral or only numerical solution is possible?