Is there any one who can help me how to sum the following summation expression? I tried but it said to many inputs. Thank you for your help!

U(x,y) = ∑[∝.ϕ1(x) + β.ϕ2(x)].ψ(y), the summation is k : 0 --> infinity. 

Where    ψ(y)=sin(kπy), b=√(1/(2ϵ)^2 +(kπ)^2 ), 

           ϕ1(x)=e^(x/(2ϵ)) (sinh(b.(1-x)))/(sinh(b)), 

           ϕ2(x)=e^((x-1)/(2ϵ)).(sinh(b.x)/(sinh(b)), 

           ∝=2/kπ (cos(0.45kπ) ), 

           β=∝.(b.e^(1/(2ϵ))/(sinh(b))⁄(1/2ϵ+b.(cosh(b)/sinh(b)))

[Geoff Hayes]

Temesegen - what said too many inputs? Please copy and paste your code and the full error message that you have observed.

[Temesgen Gelaw]

Dear Geoff

First, I write like this

syms x y k v

Hk = sinh(k*pi*y);

bk = sqrt(1/(2*v).^2 + (k*pi).^2);

Qlk = exp(x/(2*v))*sinh(bk*(1-x))/sinh(bk);

Q2k = exp((x-1)/(2*v))*sinh(bk*x)/sinh(bk);

Ck = 2*(cos(0.45*k*pi)-cos(0.55*k*pi))/(k*pi);

Bk = Ck*((bk*exp(1/(2*v))/sinh(bk)))/(1/(2*v) + bk*cosh(bk)/sinh(bk));

U = (Ck*Qlk + Bk*Q2k)*Hk;

u = symsum(U, k, 1, Inf);

Then I got this

u = -sum((exp(pi*k*y)/2 - exp(-pi*k*y)/2)*((exp(x/(2*v))*(exp((1/(4*v^2) + pi^2*k^2)^(1/2)*(x - 1))/2 - exp(-(1/(4*v^2) + pi^2*k^2)^(1/2)*(x - 1))/2)*(exp(-(pi*k*9*i)/20) + exp((pi*k*9*i)/20) - exp(-(pi*k*11*i)/20) - exp((pi*k*11*i)/20)))/(pi*k*(exp((1/(4*v^2) + pi^2*k^2)^(1/2))/2 - exp(-(1/(4*v^2) + pi^2*k^2)^(1/2))/2)) - (exp((x - 1)/(2*v))*exp(1/(2*v))*(exp(x*(1/(4*v^2) + pi^2*k^2)^(1/2))/2 - exp(-x*(1/(4*v^2) + pi^2*k^2)^(1/2))/2)*(1/(4*v^2) + pi^2*k^2)^(1/2)*(exp(-(pi*k*9*i)/20) + exp((pi*k*9*i)/20) - exp(-(pi*k*11*i)/20) - exp((pi*k*11*i)/20)))/(pi*k*(exp((1/(4*v^2) + pi^2*k^2)^(1/2))/2 - exp(-(1/(4*v^2) + pi^2*k^2)^(1/2))/2)^2*(1/(2*v) + ((1/(4*v^2) + pi^2*k^2)^(1/2)*(exp((1/(4*v^2) + pi^2*k^2)^(1/2))/2 + exp(-(1/(4*v^2) + pi^2*k^2)^(1/2))/2))/(exp((1/(4*v^2) + pi^2*k^2)^(1/2))/2 - exp(-(1/(4*v^2) + pi^2*k^2)^(1/2))/2)))), k == 1..Inf)

And then I tried as below

u = -sum((exp(pi*k*y)/2 - exp(-pi*k*y)/2)*((exp(x/(2*v))*(exp((1/(4*v^2) + pi^2*k^2)^(1/2)*(x - 1))/2 - exp(-(1/(4*v^2) + pi^2*k^2)^(1/2)*(x - 1))/2)*(exp(-(pi*k*9*i)/20) + exp((pi*k*9*i)/20) - exp(-(pi*k*11*i)/20) - exp((pi*k*11*i)/20)))/(pi*k*(exp((1/(4*v^2) + pi^2*k^2)^(1/2))/2 - exp(-(1/(4*v^2) + pi^2*k^2)^(1/2))/2)) - (exp((x - 1)/(2*v))*exp(1/(2*v))*(exp(x*(1/(4*v^2) + pi^2*k^2)^(1/2))/2 - exp(-x*(1/(4*v^2) + pi^2*k^2)^(1/2))/2)*(1/(4*v^2) + pi^2*k^2)^(1/2)*(exp(-(pi*k*9*i)/20) + exp((pi*k*9*i)/20) - exp(-(pi*k*11*i)/20) - exp((pi*k*11*i)/20)))/(pi*k*(exp((1/(4*v^2) + pi^2*k^2)^(1/2))/2 - exp(-(1/(4*v^2) + pi^2*k^2)^(1/2))/2)^2*(1/(2*v) + ((1/(4*v^2) + pi^2*k^2)^(1/2)*(exp((1/(4*v^2) + pi^2*k^2)^(1/2))/2 + exp(-(1/(4*v^2) + pi^2*k^2)^(1/2))/2))/(exp((1/(4*v^2) + pi^2*k^2)^(1/2))/2 - exp(-(1/(4*v^2) + pi^2*k^2)^(1/2))/2)))), k,1,Inf);

But the answer is Too many input arguments.

[Image Analyst]

I don't have the symbolic Toolbox so I can't help you other than to suggest this link: read this

But you must have overlooked Geoff's suggestion " the full error message" since I don't see the error message. You need to give ALL THE RED TEXT including lines numbers, line of code, etc.

Answer 1

[Roger Stafford]

The first result with ‘symsum’ very likely indicates that ‘symsum’ is unable to compute this particular infinite sum.

The second result indicating too many input arguments refers to the ‘sum’ function. See:

   http://www.mathworks.com/help/matlab/ref/sum.html

The ‘sum’ function is not symbolic but is numeric instead, and the arguments you gave, namely k,1,Inf, are inappropriate. You need to make ‘k’ a vector and unfortunately it has to be of finite length so you can only approximate an infinite sum with this method.

[Temesgen Gelaw]

Thank you very much Roger !