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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.)
##### Keywords:
dilogarithms; psi-function
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##### References:
 [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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