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

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

• Incomplete gamma function