MATLAB: Double sum of this formula

double summationMATLAB

Hello

I need help about this formula:

_{E_n}=\sum_{k=1}^{n}\left ( _{d_k} \sum_{l=0}^{1-k}_{K_l}*{sin^{2l}{b_n_-_1}}\right )

Values of K0 and b0 are known

Thanks

Best Answer

Just verify once if this is the formula that you needed. You would have to define K, b and n beforehand.

symsum((d(k).*symsum((K(l)*((sin(b(n-1))).^(2.*l))),l,0,(1-k))),k,1,n)

Doc for Symbolic Summation : https://www.mathworks.com/help/symbolic/symbolic-summation.html

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MATLAB: Sum up just the even terms of a series

Make the change of indices p=2*k and sum over k=0,1,2,...,Inf.

So, for your example

   sum_{p even} (1/p) = sum_k 1/(2*k)
                      = 1/2 *sum_k(1/k)
                      = Inf

MATLAB: Storing output (which are matrices) of for loops

Array preallocation works for me:

l = 1;
B = [0.0250; 0.0500; 0.0750; 0.1000; 0.1250; 0.1500; 0.1750; 0.2000; 0.2250; 0.2500; 0.2750; 0.3000; 0.3250; 0.3500; 0.3750; 0.4000];
B = 0.025:0.025:0.4;
kV = nan(1,1,numel(B));
CM = nan(2,4,numel(B));
rig = 0.01;
for j = 1:numel(B)                          
    k = B(j)/(2*rig);                     
    TMP = [cos(k*l)^2,        (sin(k*l)*cos(k*l))/k, sin(k*l)*cos(k*l),    (sin(k*l)^2)/k;      
        -k*sin(k*l)*cos(k*l), cos(k*l)^2,            -k*sin(k*l)^2,        sin(k*l)*cos(k*l); 
        -sin(k*l)*cos(k*l),   -(sin(k*l)^2)/k,       cos(k*l)^2,           (sin(k*l)*cos(k*l))/k;
        k*sin(k*l)^2,         -sin(k*l)*cos(k*l),    -k*sin(k*l)*cos(k*l), cos(k*l)^2];
    TMP = TMP*TMP;
    CM(:,:,j) = [TMP(1,:);TMP(3,:)];
    kV(j) = k;
end

Best Answer

Related Solutions

MATLAB: Sum up just the even terms of a series

MATLAB: Storing output (which are matrices) of for loops

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