An Introduction to Thermal Physics · Problem B.8

Systems of Interacting Particles — Daniel Schroeder

Physics — Statistical Mechanics · gamma-function

Problem

Evaluate

\Gamma(\frac{1}{2})

. (Hint: Change variables to convert the integrand to a Gaussian.) Then use the recursion formula to evaluate

\Gamma(\frac{3}{2})

and

\Gamma(-\frac{1}{2})