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Zbl 1093.33010
Alzer, Horst; Karayannakis, Dimitri; Srivastava, H.M.
Series representations for some mathematical constants. (English)
[J] J. Math. Anal. Appl. 320, No. 1, 145-162 (2006). ISSN 0022-247X

Authors' abstract: The authors apply a classical series identity involving the psi (or digamma) function with a view to deriving series representations for a number of known mathematical constants. Several closely-related consequences and results are also considered.
[H. S. P. Shrivastava (Ratlam)]

MSC 2000:: *33D99 Basic hypergeometric functions
33E20 Functions defined by series and integrals
26A33 Fractional derivatives and integrals (real functions)

Keywords: series representations; psi (or digamma) function; fractional calculus; Hurwitz (or generalized) zeta function; special functions; summation of series; Gauss hypergeometric function; polygamma function; normalized binomial mid-coefficients; harmonic numbers; $\pi$; $\pi^{2}$; $\pi^{3}$; $\pi^{4}$; $\log 2$; $\log 3$; Catalan's constant; Apéry's constant

Cited in: Zbl 1234.11022 Zbl 1198.05010

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