Infinite symsum returns symbolic number.

Hello, I would like to compute the following code:

syms n
x=0.5;
y=1.5;

f = (400/sinh(2*n*pi))*(((n*pi)*(1-(((-1)^n)*cos(1))))/((1-(n*pi)^2)^2))*(sin(n*pi*x).*sinh(n*pi*y));
%T= 273.15 + symsum(f,n,1,100);
T = 273.15 + symsum(f,n,1,inf);

When computing with a finite limit (like 100), it returns a single number.

but when computing with the infinite, it returns:

T =
 
5463/20 - 400*pi*symsum((n*sin((pi*n)/2)*sinh((3*pi*n)/2)*((1216652631687587*(-1)^n)/2251799813685248 - 1))/(sinh(2*pi*n)*(n^2*pi^2 - 1)^2), n, 1, Inf)

I have tried using vpa(T) to check the number, but it still returns a symbolic number with vpasum..

Can you let me know how to get a finite answer?

Thank you so much in advance!

Answer 1

[Walter Roberson]

I do not know why that happens, but do this for a workaround:

syms n
x=0.5;
y=1.5;

f = (400/sinh(2*n*pi))*(((n*pi)*(1-(((-1)^n)*cos(1))))/((1-(n*pi)^2)^2))*(sin(n*pi*x).*sinh(n*pi*y));
syms N positive
assumeAlso(N, 'integer');
f1 = subs(f,4*N-3);
f2 = subs(f,4*N-2);   % is zero!
f3 = subs(f,4*N-1);
f4 = subs(f,4*N);     % is zero!
fall = f1+f2+f3+f4;

%T= 273.15 + symsum(f,n,1,100);
T = 273.15 + vpa(symsum(fall,N,1,inf))

T = 

278.2575916829920971963474063102

[Jongan Park]

wow it is a very interesting approach. I dont know why and how that works.

I guess f2 and f4 are zero because the sin(n*pi*x) term goes zero.

Thank you so much for your help and time.

I was about to compromise with a summation to n=1000.

Answer 2

[Jongan Park]

I found a similar question!

and it was answered well.

https://www.mathworks.com/matlabcentral/answers/479330-need-to-find-sum-of-an-infinite-series-in-matlab-output-is-something-weird-and-not-understandable