Transport function: Difference between revisions
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In [[mathematics]] and the field of [[transportation theory (mathematics)|transportation theory]], the '''transport functions''' ''J''(''n'',''x'') are defined by | In [[mathematics]] and the field of [[transportation theory (mathematics)|transportation theory]], the '''transport functions'''<ref>{{cite web |title=transport in nLab |url=https://ncatlab.org/nlab/show/transport |website=ncatlab.org |access-date=14 July 2025 |language=en}}</ref> ''J''(''n'',''x'') are defined by | ||
:<math>J(n,x) = \int_0^x t^n \frac{e^t}{(e^t - 1)^2}\,dt.</math> | :<math>J(n,x) = \int_0^x t^n \frac{e^t}{(e^t - 1)^2}\,dt.</math> | ||
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:<math>\frac{e^t}{(e^t - 1)^2} = \sum_{k=0}^\infty k\,e^{kt}.</math> | :<math>\frac{e^t}{(e^t - 1)^2} = \sum_{k=0}^\infty k\,e^{kt}.</math> | ||
== See also == | == See also == | ||
* [[Incomplete gamma function]] | * [[Incomplete gamma function]] | ||
{{ | == References == | ||
{{Reflist}} | |||
[[Category:Special functions]] | [[Category:Special functions]] | ||
[[Category:Transportation theory]] | [[Category:Transportation theory]] | ||
{{Mathanalysis-stub}} | |||
Latest revision as of 14:30, 14 July 2025
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In mathematics and the field of transportation theory, the transport functions[1] J(n,x) are defined by
Note that
See also
References
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