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Series and product representations for some mathematical constants

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Abstract

We present several series and product representations for γ, π, and other mathematical constants. One of our results states that, for all real numbers µ s>0, we have

$$ \gamma = \sum\limits_{k = 0}^\infty {\frac{1} {{(1 + \mu )^{k + 1} }}\sum\limits_{m = 0}^k {\left( {_m^k } \right)} \left( { - 1} \right)^m \mu ^{k - m} S(m),} $$

where S(m) = ∑ ∞ k=1 1/2k+m.

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Authors and Affiliations

  1. Morsbacher Str. 10, D-51545, Waldbröl, Germany

    Horst Alzer

  2. Department of Mathematics and Statistics, The University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus

    Stamatis Koumandos

Authors
  1. Horst Alzer
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  2. Stamatis Koumandos
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Correspondence to Horst Alzer.

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Communicated by Attila Pethő

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Alzer, H., Koumandos, S. Series and product representations for some mathematical constants. Period Math Hung 58, 71–82 (2009). https://doi.org/10.1007/s10998-009-9071-3

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  • DOI: https://doi.org/10.1007/s10998-009-9071-3

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