i'm doing something called Sommerfeld expansion i got somehelp online source i will show after code. Sommerfeld expansion to integrate Fermi Dirac-Dirac equation to find total number of particles N for energy i define to be x.
The problem is sometimes either of my integral eq1 or eq2 dosn't work! i need them to be evaluated. can someone help please! Thanks in Advanceadvance.
Here is the Codecode
Clear["Global`*"]
f[x_] := 1/(Exp[(x - u)/(k*t)] + 1);
h[x] = -D[f[x], x];
g1 = Normal[Series[g[x], {x, u, 7}]];
g2 = Normal[Series[g[x], {x, u, 10}]];
g3 = g2 - g1;
G1 = Simplify[g1*h[x] /. {x -> u + k*t*y}];
G2 = Simplify[g3*h[x] /. {x -> u + k*t*y}];
eq1 = Simplify[k*t*Integrate[G1, {y, -Infinity, Infinity},
Assumptions -> {k > 0, t > 0}]]
eq2 = Simplify[k*t*Integrate[G2, {y, -Infinity, Infinity},
Assumptions -> {k > 0, t > 0}]]
f1 = PowerExpand[eq1 + eq2]
I just did the same! but no result!?
the result should be given as in last lines here