# Help with a double series?

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DIANA CARTLON on 28 Nov 2019
Commented: Walter Roberson on 18 Apr 2021
I am trying to write function for the equation, can someone tell me what i am doing wrong
clear,clc
E=input('Please enter the Modulus of Eleasticity, E\n');
v=input('Please enter the Poisson Ratio, v\n');
rec_plate_pt(a,b,P,xo,yo,x,y);
D=(E*h^3)/(12*(1-v^2))
c=(4*P)/(pi^4*a*b*D)
function w = rec_plate_pt(a,b,P,xo,yo,x,y)
s=0;
for m=1:Inf
for n=1:Inf
s=c*(sin((m*pi*xo)/a)*sin((n*pi*yo)/b)/((m^2/a^2+n^2/b^2).^2)*(sin((m*pi*x)/a))*(sin(n*pi*y)/b))
format long
fprintf('%d',w);
end
end
end Walter Roberson on 28 Nov 2019
Those are infinite series. You should use symsum()

Jyothis Gireesh on 30 Dec 2019
As Walter mentioned in the previous comment the double summation may be implemented using a combination of symbolic variables and the symsum()” in MATLAB instead of defining a function.
One possible implementation is given below
syms Wc(x,y) m n;
Wc(x,y) = c*symsum(symsum(sin(m*pi*x0/a)*sin(n*pi*y0/b)*sin(m*pi*x/a)*sin(n*pi*y/b)/(m^2/a^2 + n^2/b^2)^2,n,1,Inf),m,1,Inf);

Johannes Ebert on 18 Apr 2021
Hello together,
I have a question: if I apply the code above with my parameter set, the result is the following:
My Input: Wc(120,200)
The result:
(7312256873090709*symsum(symsum(((exp(-(pi*n*10i)/31)*1i)/2 - (exp((pi*n*10i)/31)*1i)/2)^2/(m^2/722500 + n^2/384400)^2, n, 1, Inf)*((exp(-(pi*m*12i)/85)*1i)/2 - (exp((pi*m*12i)/85)*1i)/2)^2, m, 1, Inf))/39614081257132168796771975168
Is there a chance to get the concret value for the used parameter set?
Thanks und kind regards,
Johannes
Walter Roberson on 18 Apr 2021
Maple is able to find an explicit formula for part2 (that is, the inner symsum() ) in terms of a fair number of psi() calls and some trig terms. But it struggles to find anything definite further than that or to simplify the mess.