An Introduction to Thermal Physics · Problem B.9

Systems of Interacting Particles — Daniel Schroeder

Physics — Statistical Mechanics · gamma-function-numerical

Problem

Carry out the integral B.12 numerically to evaluate Γ(13)\Gamma(\frac{1}{3}) and Γ(23)\Gamma(\frac{2}{3}). A useful identity whose proof is beyond the scope of this book is Γ(n)Γ(1−n)=πsin⁡(nπ).\Gamma(n)\Gamma(1-n) = \frac{\pi}{\sin(n\pi)}. Check this formula numerically for n=1/3n = 1/3.

Browse the problem library