Code keeps running and running and not stopping

I have code I am trying to run and when I try to get the value for V_max, the code won't stop running. I don't get an error and it will run for hours if I let it. I have asked my TA for my class as well as several classmates and none of them can figure out what is wrong either.

    h=4.136e-15;%eVs
k=8.617e-5;%eV/k
c=3e8;
theta_s=0.00467;%radians
T_c=300;
q=1.6e-19;
syms E;
%PROBLEM 1
%a
T_s=5760;
a=q*(pi/2)*(1-cos(2*theta_s))*(2/((h^3)*(c^2)));
fun1= ((E.^3)./((exp(E/(k*T_s)))-1));
Pin= a*(int(fun1,0,inf));%input power 
Intensity=double(Pin); %W/m^2
%Intensity= 1.3570e3 W/m^2, this is almost the exact number for the actual 
%power,which is 1350 W/m^2, just over by 7
%b
E_g=1.43;%eV
fun2= (E.^2)./((exp(E/(k*T_s))-1));
J_l= a*int(fun2,E_g,inf);%light generated current density
%c
theta_e=pi/2;
b=q*(pi/2)*(1-cos(2*theta_e))*(2/(h^3)*(c^2));
fun3= (E.^2)./(exp(E/(k*T_c))-1);
J_0= b*int(fun3,E_g,inf);%reverse saturation current density
%d
syms V;
P= V*(J_l + J_0*(exp((q*V)/(k*T_c))-1));
V_max=double(solve(P,V));
J_max= (J_l + J_0*(exp((q*V)/(k*T_c))-1));

V_max is the part of the code that is giving me problems and I can't figure out what is wrong. Please help me. Thank you!

[Rik]

I don't have much experience with the solve function, but I would have thought it would time out after a while, if it is a too complicated formula.

[Savanna]

that's what I thought too, but I had it running last night and even then it wouldn't stop running-it was running for about 8-9 hours and still nothing.

[Walter Roberson]

solve() has no timeout.

[Savanna]

ok then how do I get it to finish running and actually solve for the variable I need?

[Walter Roberson]

You cannot: your formulae generate infinities.

[Walter Roberson]

... though I am finding hints that the infinities might be false constructs... checking more...

[Savanna]

ok I'm just a bit confused since I am just copying a formula from a textbook into matlab with the limits for the integral are E=E_g to E=infinity. The other people in my class have something similar, but haven't run into this problem like I have.

[Walter Roberson]

I have determined that fun2 and fun3 do have closed-form integrals in the form specified, but I am still working on characterizing them.

Answer 1

[Walter Roberson]

Your J_l and J_0 both have limit() operations that look to me as if they suggest non-convergence. Trying to solve() under those conditions is going to be a failure.

Maple says that the integral of fun2 and fun3 are complex infinity; when I prod it a different way, it says the limit as E approaches infinity is undefined, as it starts to involve negative infinity plus infinity.

You should recheck your formula.