1. ## 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]
$
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

2. 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 $u=x/2$.

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?

4. I'm not sure. Sorry. Looks then to me $a$ needs to be greater than $3$.

5. ## Re: please if you know about elliptic integrals I NEED help!

I want to solve this eqn using the elliptic integral
int(1/sqrt(1-ksin(phi)))

6. ## Re: please if you know about elliptic integrals I NEED help!

Originally Posted by prash
I want to solve this eqn using the elliptic integral
int(1/sqrt(1-ksin(phi)))
do you mean

$$\int \frac{1}{\sqrt{1- k\sin(\phi)}}d\phi$$

if so it's

$$-\frac{2 F\left(\frac{1}{4}(\pi-2\phi),\frac{2k}{k-1}\right) \sqrt{\frac{k\sin(\phi)-1}{k-1}}}{\sqrt{1-k\sin(\phi)}}$$

$$F(\phi,m)\mbox{ is the elliptic integral of the first kind.}$$

7. ## Re: please if you know about elliptic integrals I NEED help!

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?

8. ## Re: please if you know about elliptic integrals I NEED help!

my mistake, getting the tex correct was a pain, it's corrected.

9. ## Re: please if you know about elliptic integrals I NEED help!

@Romsek,Can u elaborate me with the proof for the solution

10. ## Re: please if you know about elliptic integrals I NEED help!

nope, I just plugged it into Mathematica and that's what came out. sorry

11. ## Re: please if you know about elliptic integrals I NEED help!

how can i have a numerical solution for the above solution?

12. ## Re: please if you know about elliptic integrals I NEED help!

If you have a new question, you should start a new thread. From the main calculus page, it's under Forum Tools -> Post a new Thread.

- Hollywood