Question: elliptic integral

Hi all,

While solving a différential equation, I encounter an integral:

> Int(1/sqrt(1-k^2*sin(s)^2), s = 0 .. phi);

                         /phi                         
                        |               1             
                        |     --------------------- ds
                        |                     (1/2)   
                       /0     /     2       2\        
                              \1 - k  sin(s) /        

with k<1.  But Maple don't want to give me the special function F(k,phi)

>value(%) assuming k < 1;

                     /          1                        \
                  int|---------------------, s = 0 .. phi|
                     |                (1/2)              |
                     |/     2       2\                   |
                     \\1 - k  sin(s) /                   /

What I found in Abramowitz, is that if phi vary from 0 to Pi/2, it's an elliptic integral of the first kind. (p. 608)

> Int(1/sqrt(1-k^2*sin(s)^2), s = 0 .. (1/2)*Pi);

                       /1/2 Pi                         
                      |                  1             
                      |        --------------------- ds
                      |                        (1/2)   
                     /0        /     2       2\        
                               \1 - k  sin(s) /        
> value(%) assuming 0 < k  < 1;

                                        /   1\
                               EllipticF|k, -|
                                        \   k/
                               ---------------
                                      k       

but I do need from 0 to phi.

In addition, there is a reference about the Jacobi elliptic function (p.569) wich is suppose to be the inverse of the integral I want to solve.

Can someone untangle this for me.

Thanks in advance

Mario