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) = \int_{0}^{x} t^{n} \frac{e^{t}}{(e^{t} - 1)^{2}} d t .

Note that

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

See also

Incomplete gamma function

References

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

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