Implementation of infinite series in MATLAB.

How I can impliment this type of infinite series in MATLAB given a function as where , here l,\gamma are constant. when I use

syms k;
exp = symsum(H(k + 1,gamma_av),k,1,Inf);

I used to get error like this "The following error occurred converting from sym to double:

Unable to convert expression into double array."

Please help me out.

[Walter Roberson]

using exp as a variable name can lead to problems.

[Walter Roberson]

How did you define H in your code?

[Sudhir Sahoo]

I have written a differnt function for H and I call that in main code.

[Walter Roberson]

The error is not in the part of the code that you posted. We need to see the rest of the code.

[Sudhir Sahoo]

@Walter Roberson Ok sir I am posting the code as follows

syms k;
snr = 2;
l = 2;
expression2 = symsum(H(k + 1,snr,l),k,1,Inf);

and my function i defined as

function [out] = H(y,z,l)
    %gam, y,z,l are user inputs
     m =  -1/log2(cos(pi/6)); % in paper its used as small gamma.(\gamma)
out1 = (2/z)^y;
out2 = gamma(y) - igamma(y,(l^(-2*(m + 2))/2)*z);
out = out1 * out2;
end

And I want to calculate the sum

Answer 1

[Walter Roberson]

The error message you get is because the symbolic engine was not able to find a convergent value for the infinite series when you use double(). And depending on the number of digits you use for vpa() it might or might not find a solution.

Interestingly, if you use a finite series such as 75 terms, then double() does well at converting the value, whereas you need on the order of 150+ digits in order for vpa to be able to resolve it: if you use a high finite Limit and too few digits then vpa() will tend to return exactly 0.

format long g
syms k;
snr = 2;
l = 2;
Limit = Inf;
expression2 = symsum(H(k + 1,snr,l),k,1,Limit);
for D = 120:129
    try
        D
        ev = vpa(expression2, D)
        ed = double(ev)
    catch ME
        fprintf('failed working at %d digits\n', D);
    end
end

D = 
   120

ev = 

failed working at 120 digits

D = 
   121

ev = 

0.000000003077984867743638419940134683770443072429756599385419397056352496391763650277668849759282913432606221931130564797576520443

ed = 
      3.07798486774364e-09

D = 
   122

ev = 

0.0000000030779848677436384199401346837704430724297565993854193970563524963917636502776688497592829134326062219311305647975746247394

ed = 
      3.07798486774364e-09

D = 
   123

ev = 

0.00000000307798486774363841994013468377044307242975659938541939705635249639176365027766884975928291343260622193113056479757456758764

ed = 
      3.07798486774364e-09

D = 
   124

ev = 

0.000000003077984867743638419940134683770443072429756599385419397056352496391763650277668849759282913432606221931130564797574605713361

ed = 
      3.07798486774364e-09

D = 
   125

ev = 

failed working at 125 digits

D = 
   126

ev = 

0.00000000307798486774363841994013468377044307242975659938541939705635249639176365027766884975928291343260622193113056479757460092717886

ed = 
      3.07798486774364e-09

D = 
   127

ev = 

0.000000003077984867743638419940134683770443072429756599385419397056352496391763650277668849759282913432606221931130564797574600914952293

ed = 
      3.07798486774364e-09

D = 
   128

ev = 

failed working at 128 digits

D = 
   129

ev = 

0.00000000307798486774363841994013468377044307242975659938541939705635249639176365027766884975928291343260622193113056479757460091191697691

ed = 
      3.07798486774364e-09

double(expression2)

Error using symengine
Unable to convert expression containing remaining symbolic function calls into double array. Argument must be expression that evaluates to number.

Error in sym/double (line 702)
Xstr = mupadmex('symobj::double', S.s, 0);

function [out] = H(y,z,l)
    Pi = sym(pi);
    %gam, y,z,l are user inputs
     m =  -1/log2(cos(Pi/6)); % in paper its used as small gamma.(\gamma)
out1 = (2/z)^y;
out2 = gamma(y) - igamma(y,(l^(-2*(m + 2))/2)*z);
out = out1 * out2;
end

Answer 2

[Sahil]

function [out] = H(y,z,l)
    Pi = sym(pi);
    %gam, y,z,l are user inputs
    m = -1/log2(cos(Pi/6));
    % in paper its used as small gamma.(\gamma)
    out1 = (2/z)^y;
    out2 = gamma(y) - igamma(y,(l^(-2*(m + 2))/2)*z);
    out = out1 * out2;
end

[Walter Roberson]

What is the difference between that and what I posted last year at https://www.mathworks.com/matlabcentral/answers/742277-implementation-of-infinite-series-in-matlab#answer_622427 ?