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[1][2]

J_n(x) = \int_0^x t^n \frac{e^t}{(e^t - 1)^2}\,dt.

Note that

\frac{e^t}{(e^t - 1)^2} = \sum_{k=0}^\infty k\,e^{kt}.

See also

References

  1. ^ Rogers, William & Powell, Robert (July 3, 1958). Tables of transport integrals. National Bureau of Standards. Retrieved 16 March 2026.
  2. ^ Galassi, Mark. GNU Scientific Library Reference Manual. 3 ed. ISBN 0954612078. Retrieved 16 March 2026.