function [V, S] = SiciakRealDisk(X,Y)
%__________________________________________________________________________
% computes the Siciak-Zaharjuta extremal function for the real unit disk
%__________________________________________________________________________
%----- INPUT-------------
% X Y    grid for evaluating the function Ex:
%        x=-L:step:L,[X,Y]=meshgrid(x,x)
% m      number of sides of polygon
%-----OUTPUT--------------
% V      V(i,j)=S(X(i,j),Y(i,j)).
%__________________________________________________________________________

% modulus of Joukowski function
Lh=@(z) 1/2.*log(abs(z+(z.^2-1).^(1/2)));
V=Lh(abs(X).^2+abs(Y).^2+abs(X.^2+Y.^2-1));

S=exp(V);
end


