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Madhusudan posted an Question

April 27, 2020 • 16:12 pm

30 points

IIT JAM
Physics (PH)

Solve integration

solve integration . I attached the problem , this create problem for solving internal energy for radation in stastical mechanics

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Ruby negi Best Answer

this is solved by residue method .. note that in the first line this is a misprint( there is z^3 instead of z^4) and the further steps are right...go through this method too.. this will help u to solve other questions too . best regards.
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z^4 instead of z^3*****
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Ruby negi

when k=1.. remember the value of zeta(4) that is π^4/15.. this value of zeta(4) is found by residue method...
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Abhishek singh

Here is the solution. Riemann Zita function is used. which is some higher mathematics. use its value directly for time being. Best regards.
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Ruby negi

solution.......
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answer is not correct
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correct answer is if k= 1 then answer is (pie)^4/15
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Abhishek singh

You can use this approximation in statistical mechanics. Solution attached.
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this is bose Einstein integral
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and without approximation answer is different
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if k =1 how we can use this approximation . because. x goes to 0 to infinity . and approximation is correct only for large value .
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Okay, wait a minute. I am attaching the solution in the next comment.
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M
Madhusudan

dx
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Ruby negi

is it dX or dK?
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dx
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