Transport function

In mathematics and the field of transportation theory, the transport functions ^[1] J(n,x) are defined by

${\displaystyle J(n,x)=\int _{0}^{x}t^{n}{\frac {e^{t}}{(e^{t}-1)^{2}}}\,dt.}$

Note that

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

See also

• Incomplete gamma function

References

1. "transport in nLab". ncatlab.org. Retrieved 14 July 2025.