Nu function
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Revision as of 22:07, 9 May 2022 by imported>MedAI (correction)
In mathematics, the nu function is a generalization of the reciprocal gamma function of the Laplace transform.
Formally, it can be defined as
- [math]\displaystyle{ \begin{align} \nu(x) & \equiv \int_0^\infty \frac{x^t \, dt}{\Gamma(t+1)} \\[10pt] \nu(x,\alpha) & \equiv \int_0^\infty \frac{x^{\alpha+t} \, dt}{\Gamma(\alpha+t+1)} \end{align} }[/math]
where [math]\displaystyle{ \Gamma(z) }[/math] is the Gamma function.[1][2]
See also
- Lambda function (disambiguation)
- Mu function
References
- ↑ Erdélyi, A; Magnus, W; Tricomi, FG; Oberhettinger, F (1981). Higher Transcendental Functions, Vol. 3: The Function y(x) and Related Functions. pp. 217–224.
- ↑ (in English) Table of Integrals, Series, and Products (8th ed.). Academic Press, Inc.. 2015. ISBN 978-0-12-384933-5.
External links
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