An Introduction to Thermal Physics · Problem B.19

Systems of Interacting Particles — Daniel Schroeder

Physics — Statistical Mechanics · riemann-zeta-function

Problem

Integrate equation B.42 twice more, then plug in x=π/2x = \pi/2 to obtain a formula for ∑odd(1/k4)\sum_{\text{odd}}(1/k^4). Use this formula to show that ζ(4)=π4/90\zeta(4) = \pi^4/90, and thus evaluate the integrals B.36 for the case n=3n = 3. Explain why this procedure does not yield a value for ζ(3)\zeta(3).

Related theory

Browse the problem library