function expand_kappa_lag1(kap,s,nmax)
% --- COEFFICIENTS FOR THE EXPANSION OF KAPPA DISTN IN LAGUERRES
% --- This illustrates the divergence of the expansion
% Fig 4.8 with kap = 30 used nmax = 25 and scale factor s = 1
format long e
xn=[1:1:nmax]; [pt,wt] = lagptwt(nmax);
wtfcn=sqrt(pt).*exp(-pt);     % Weight function
spt=s*pt;                     % SCALE THE POINTS
swt=s*wt./wtfcn';             % SCALE THE BIG WEIGHTS
a=[];
p1=ones(1,nmax); a=[a p1'];             % *** L_0(x)
p2=1.5*ones(1,nmax)-spt'; a=[a p2'];    % *** L_1(x)
% --- L_n(x) BY RECURRENCE
for n=3:nmax
    nm1=n-1;
    p3=(2*nm1-0.5-spt').*p2/nm1 - (nm1-.5)*p1/nm1; 
    a=[a p3']; p1=p2; p2=p3;
end
kapp1=kap+1;
norm=2*pi*gamma(kapp1)/((sqrt(pi*kapp1)^3)*gamma(kap-0.5));
%kappa=sqrt(spt)'.*(1/(1+spt./kapp1)).^kapp1; % *** Kappa distn
for i=1:nmax
    kappa(i)=sqrt(spt(i))*(1/(1+spt(i)/kapp1))^kapp1;
end
% --- CALCULATE THE EXPANSION COEFFICIENTS BY QUADRATURE
for n=1:nmax
    nm1=n-1;
    c(n)=sum(swt.*(kappa.*a(:,n)'))*factorial(nm1)/gamma(nm1+3/2);
end
% Plot the coefficients
plot(xn(3:1:15),c(3:1:15),'-ok','linewidth',1.6,'markersize',7,'markerfacecolor','k')
hold off
%axis('FontSize', 24)
axis([3 15 -.1 .2])
set(gca,'FontSize',15)
set(gca,'Ytick',[-.1:.05:.2],'linewidth',1.6)
set(gca,'Xtick',[3:3:15],'linewidth',1.6)
%axis([-3 3 -1 1.2])
xlabel('$n$','Interpreter','LaTex','FontSize',30)
ylabel('$c_n$','Interpreter','LaTex','FontSize',30)
str1 = {'$\kappa = 30$'};
text(9,.15,str1,'Interpreter','Latex','Fontsize',26)
end
% Laguerre quadrature weights and points
function [pt,wt] = lagptwt(n)
xn=[0:1:n-1]; a=2*xn+3/2; b=(xn.*(xn+1/2)); % Recurrence coefficients
rtb=sqrt(b); rtb(1)=[];
t=diag(rtb,-1)+diag(a)+diag(rtb,1); % Jacobi matrix
[f,lambda]=eig(t);
pt=diag(lambda);
wt=gamma(3/2)*f(1,:).^2
ptwt=[pt,wt'];
end