In mathematics, the nu function is
\( {\displaystyle {\begin{aligned}\nu (x)&\equiv \int _{0}^{\infty }{\frac {x^{t}\,dt}{\Gamma (t+1)}}\\[10pt]\nu (x,\alpha )&\equiv \int _{0}^{\infty }{\frac {x^{\alpha +t}\,dt}{\Gamma (\alpha +t+1)}}\end{aligned}}} \)
where \( \Gamma (z) \) is the Gamma function.[1][2]
This generalize the Laplace transform of the reciprocal gamma function.
See also
Lambda function (disambiguation)
Mu function
References
Erdélyi, A, Magnus, Tricomi, F. G, W, Oberhettinger (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. (8 ed.). Academic Press, Inc. ISBN 978-0-12-384933-5. LCCN 2014010276.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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