Evaluation of Some Transport Integrals

The transport integrals ${\int }_0^{\infty }{x}^{\text{2n}}{\mathrm{(x}}^2{\mathrm{+a}}^2{)}^{\text{−1}}{e}^x{\mathrm{(e}}^x{\text{±1)}}^{\text{−2}}\mathrm{\hspace{0.17em}dx}$ for Fermi‐Dirac (+) and Bose‐Einstein (−) statistics are expressed simply in terms of tabulated functions. Some examples from the theory of lattice thermal conductivity and electron‐electron collisions in metals are discussed. The related integrals ${\int }_0^{\infty }{\mathrm{\hspace{0.17em}x}}^{\text{2n+1}}{\mathrm{(x}}^2{\mathrm{+a}}^2{)}^{\text{−1}}{\mathrm{(e}}^x{\text{±1)}}^{\text{−1}}\mathrm{\hspace{0.17em}dx}$ are also evaluated.