Transport integrals

In mathematics and statistical physics, the transport integrals (sometimes transport functions) are a family of special functions arising in the theory of transport phenomena of solids.

Definition

The transport integrals are defined by the integral representation

$J_n(x)=\underset{0}{\overset{x}{\int }}{t}^n\frac{e^t}{(e^t-1{)}^2}dt.$

Note that

$\frac{e^t}{(e^t-1{)}^2}=\sum _{k=0}^{\mathrm{\infty }}k{e}^{kt}.$

See also

• Incomplete gamma function