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On some series containing \(\psi{}(x)-\psi{}(y)\) and \((\psi{}(x)- \psi{}(y))^ 2\) for certain values of \(x\) and \(y\). (English) Zbl 0782.33001
The article under review discusses series containing the factors \(\psi(k)- \psi(1)\), \((\psi(k)-\psi(1))^ 2\), \(\psi({1\over 2}\pm k)- \psi({1\over 2})\) and \(\psi({1\over 2}(k+1)-\psi({1\over 2}k)\) with \(k\in\mathbb{N}\). Here \(\psi(x)=d/dx \log \Gamma(x)\) where \(\Gamma(x)\) is the gamma function [see L. Lewin, Polylogarithms and associated functions (1981; Zbl 0465.33001)].

MSC:
33B15 Gamma, beta and polygamma functions
40A25 Approximation to limiting values (summation of series, etc.)
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[1] Gradshteyn, I.S.; Ryzhik, I.M., Tables of integrals, series and products, (1965), Academic Press New York · Zbl 0918.65002
[2] Hansen, E.L., A table of series and products, (1975), Prentice-Hall, Englewood Cliffs, NJ
[3] Lewin, L., Polylogarithms and associated functions, (1981), North-Holland Amsterdam · Zbl 0465.33001
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