%asn

%asn — elliptic integral

Calling sequence

[y]=%asn(x,m)

Parameters

`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!

Author

F. D.