The provided code indeed calculates the 
and 
matrices based on the given formula. Here's an alternative approach that doesn't require declaring 'stirling1' as a separate function.
and matrices based on the given formula. Here's an alternative approach that doesn't require declaring 'stirling1' as a separate function.function Td1 = compute_Td1(M)
% Create a matrix of binomial coefficients
[I, J] = ndgrid(1:M, 1:M);
binomials = zeros(M, M);
for i = 1:M
binomials(i, 1:i) = arrayfun(@(ii, jj) nchoosek(ii-1, jj-1), I(i, 1:i), J(i, 1:i));
end
% Create a matrix for powers
powers = ((- (M - 1) / 2) .^ (I - J)) .* (J <= I);
% Element-wise multiplication to get Td1
Td1 = binomials .* powers;
end
function Td2 = compute_Td2(M)
% Initialize Td2 with identity
Td2 = eye(M+1);
for n = 2:M+1
for k = 2:n-1
Td2(n, k) = Td2(n-1, k-1) - (n-2) * Td2(n-1, k);
end
end
Td2 = Td2(2:M+1, 2:M+1);
end
% Example usage:
Td1 = compute_Td1(M);
disp('T_d^1:');
disp(Td1);
Td2 = compute_Td2(M);
disp('T_d^2:');
disp(Td2);
Additionally, for implementing cross products, consider using MATLAB's 'cross' function instead of nested for loops. You can find the relevant documentation here:
I believe this will be of use!
