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My integral eq1 doesn't Evaluate so my power expandevaluate

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 enter image description here

My integral eq1 doesn't Evaluate so my power expand

i'm doing something called Sommerfeld expansion i got somehelp online source i will show after code. Sommerfeld expansion to integrate Fermi 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 Advance.

Here is the Code

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 enter image description here

My integral doesn't evaluate

i'm doing something called Sommerfeld expansion i got somehelp online source i will show after code. Sommerfeld expansion to integrate Fermi-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 advance.

Here is the code

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 enter image description here

added 265 characters in body
Source Link
user63891
user63891

i'm doing something called Sommerfeld expansion i got somehelp online source i will show after code. Sommerfeld expansion to integrate Fermi 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 Advance.

Here is the Code

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 enter image description here

i'm doing something called Sommerfeld expansion to integrate Fermi 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 Advance.

Here is the Code

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'm doing something called Sommerfeld expansion i got somehelp online source i will show after code. Sommerfeld expansion to integrate Fermi 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 Advance.

Here is the Code

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 enter image description here

Source Link
user63891
user63891
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