Abstract
This section is recorded by MIPT students Petrova Elena and Ivanenko Aleksei. It is about the properties of the \(\Gamma \)-function, which are used in the other sections of this book.
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E.g. in the case of the previous relation one could compare the analytic properties of 1/z and \(\Gamma (z)/\Gamma (z+1)\) functions. Note that one cannot do the same for \(\Gamma (z+1)\) and \(z\, \Gamma (z)\), because these functions are not analytic at \(z=\infty \), as we will see below in the Sect. 2.3. Note that \(e^{1/z}\) is not analytic at \(z=0\). Similarly \(e^z\) is not analytic at infinity, because the proper coordinate at infinity is \(w = 1/z\).
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Akhmedova, V., Akhmedov, E.T. (2019). \(\Gamma \)-Function. In: Selected Special Functions for Fundamental Physics. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-35089-5_2
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DOI: https://doi.org/10.1007/978-3-030-35089-5_2
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