%asn

elliptic integral

Calling Sequence

[y]=%asn(x,m)

Arguments

:x upper limit of integral ( x>0) (can be a vector) : :m parameter of integral ( 0<m<1) : :y value of the integral :

Description

Calculates the elliptic integral

If x is a vector, y is a vector of same dimension as x.

Examples

m=0.8;z=%asn(1/`sqrt`_(m),m);K=`real`_(z);Ktilde=`imag`_(z);
x2max=1/`sqrt`_(m);
x1=0:0.05:1;x2=1:((x2max-1)/20):x2max;x3=x2max:0.05:10;
x=[x1,x2,x3];
y=%asn(x,m);
rect=[0,-Ktilde,1.1*K,2*Ktilde];
`plot2d`_(`real`_(y)',`imag`_(y)',1,'011',' ',rect)

`deff`_('y=f(t)','y=1/sqrt((1-t^2)*(1-m*t^2))');
`intg`_(0,0.9,f)-%asn(0.9,m)  //Works for real case only!