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]

$\displaystyle

du/SQRT(1 - (ksinu)^2)

$

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!

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)))

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

Quote:

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

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

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

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?

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

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

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

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

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

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

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

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