Transport function

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

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

These functions are applied in optimization problems within transportation theory, such as determining optimal transport plans and minimizing costs. They help model various aspects of these problems, providing analytical tools for efficient decision-making.

Note that

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

References

• Solving a multi-objective solid transportation problem: a comparative study of alternative methods for decision-making. Journal of Engineering and Applied Science. Retrieved from [link](https://jeas.springeropen.com/articles/10.1186/s44147-021-00014-w).

See also

• Incomplete gamma function