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#
# landen.m
#
# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
N = 10;
function retval = M(a,b)
for i = (1:10)
A = (a+b)/2;
b = sqrt(a*b);
a = A;
endfor
retval = a;
endfunction;
function retval = EllipticKk(k)
retval = pi / (2 * M(1, sqrt(1-k^2)));
endfunction
k = 0.5;
kprime = sqrt(1-k^2);
EK = EllipticKk(k);
EKprime = EllipticKk(kprime);
u = EK + EKprime * i;
K = zeros(N,3);
K(1,1) = k;
K(1,2) = kprime;
K(1,3) = u;
format long
for n = (2:N)
K(n,1) = (1-K(n-1,2)) / (1+K(n-1,2));
K(n,2) = sqrt(1-K(n,1)^2);
K(n,3) = K(n-1,3) / (1 + K(n,1));
end
K(:,[1,3])
pi / 2
scd = zeros(N,3);
scd(N,1) = sin(K(N,3));
scd(N,2) = cos(K(N,3));
scd(N,3) = 1;
for n = (N:-1:2)
nenner = 1 + K(n,1) * scd(n, 1)^2;
scd(n-1,1) = (1+K(n,1)) * scd(n, 1) / nenner;
scd(n-1,2) = scd(n, 2) * scd(n, 3) / nenner;
scd(n-1,3) = (1 - K(n,1) * scd(n,1)^2) / nenner;
end
scd(:,1)
cosh(2.009459377005286)
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