In mathematics, the nu function is a generalization of the reciprocal gamma function of the Laplace transform.
Formally, it can be defined as
![{\displaystyle {\begin{aligned}\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{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c81e17bbea7685e1fd08aa86d0efb3362d774dd4)
where is the Gamma function. [1] [2]
See also
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.
- ^ Gradshteyn, Izrail Solomonovich; Ryzhik, Iosif Moiseevich; Geronimus, Yuri Veniaminovich; Tseytlin, Michail Yulyevich; Jeffrey, Alan (2015) [October 2014]. Zwillinger, Daniel; Moll, Victor Hugo (eds.). Table of Integrals, Series, and Products. Translated by Scripta Technica, Inc. (8th ed.). Academic Press, Inc. ISBN 978-0-12-384933-5. LCCN 2014010276.