(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The Bloch-Gruneissen approximation for the resistance on a monovalent metal is

[tex]\rho[/tex]=C(T[tex]^{5}[/tex]/[tex]\Theta[/tex][tex]^{6}[/tex])[tex]\int[/tex][tex]^{\Theta/T}_{0}[/tex][tex]\frac{x^{5}dx}{(e^{x}-1)(1-e^{-x})}[/tex]

(a)For T->[tex]\infty[/tex], show that [tex]\rho[/tex]=(C/4)(T/[tex]\Theta^{2}[/tex])

(b)For T->0, show that [tex]\rho[/tex]=5![tex]\zeta(5)[/tex]C[tex]\frac{T^{5}}{\Theta^{6}}[/tex]

2. Relevant equations

The section is on Bernoulli numbers and the Euler-Maclaurin Formula. Several definitions including x/(e^x-1)=sum->(Bn*x^n)/n!, Bernoulli Polynomials, Reimann-Zeta function, etc.

3. The attempt at a solution

For part (a) I see that as T->infinity the upper integration limit goes to zero, thus I may approximate the integrand giving (as the integrand) x^5/[(x+x^2/2!+x^3/3!+...)(-x+x^/2!-x^3/3!+...)]. Can I just multiply this out, simplify, and integrate term by term? If so, over what integration limits?

For part (b) the upper limit goes to infinity so I'm guessing I need to do the integral by substituting some definition of the Bernoulli Numbers?...

Help....

PS - Sorry if the equations are unclear. I'm new to LaTex. Help with that would be appreciated too.

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# Homework Help: Bernoulli Numbers, Euler-Maclauring Formula - Math Methods class

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