Intergrating from negative infinity to infinity

Hello,

I am trying to solve an equation where limits of intergration are from negative infinity to infinity.

function damp = pmb(zeta)
syms zeta
mu=4*pi*10.^-7;i=1;v=10;w=0.001;%t=0.05; r=0.032;
sigma= 5.8*10.^7; a=mu*sigma;  h=0.05;p=0.01; lp=0.1;
k=sqrt(((zeta).^2)+(i*zeta*a*v));
H=(((zeta).^2)./(((zeta).^2)+(k.^2)+(2*abs(zeta)*k*coth(k*w))));

x1=exp(-(abs(zeta))*p); x2=exp(-(abs(zeta))*h);
n=3;
for I=1:n
    e1=exp(i*zeta*(1+lp)); e2=exp(i*zeta*1);
    jr=(1./(4*pi*((zeta).^2))).*(e1-e2)*(-i).^(n-1);
    
end
A=jr*mu*(1-x1)*x2;
z=(abs(zeta*A)).^2;
S= z*real(H);
end

i get the following error, while using quad function damp=quad('pmb',-inf,inf)

"The integrand function must return an output vector of the same length as the input vector."

Answer 1

[Chunru]

The following correct the syntax error in your original program. You need to check/debug the function definition to ensure it is integratable.

y=integral(@pmb,-inf,inf)

Warning: Inf or NaN value encountered.

y = Inf

function S = pmb(zeta)
    %syms zeta
    mu=4*pi*10.^-7; i=1;v=10; w=0.001;%t=0.05; r=0.032;
    sigma= 5.8*10.^7; a=mu*sigma;  h=0.05; p=0.01; lp=0.1;
    k=sqrt(((zeta).^2)+(i*zeta*a*v));
    
    H=(((zeta).^2)./(((zeta).^2)+(k.^2)+(2*abs(zeta).*k.*coth(k*w))));
    x1=exp(-(abs(zeta))*p); x2=exp(-(abs(zeta))*h);
    n=3;
    for I=1:n
        e1=exp(i*zeta*(1+lp)); e2=exp(i*zeta*1);
        %whos
        jr=(1./(4*pi*((zeta).^2))).*(e1-e2)*(-i).^(n-1);
        
    end
    A=mu*jr.*(1-x1).*x2;
    z=(abs(zeta.*A)).^2;
    S= z.*real(H);
    %whos
    %pause
end