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“School of Mathematics”

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Paper   IPM / M / 11495
School of Mathematics
  Title:   Vacca-type series for values of the generalized Euler constant function and its derivative
  Author(s): 
1.  Kh. Hessami Pilehrood
2.  T. Hessami Pilehrood
  Status:   Published
  Journal: Journal of Integer Sequences
  Vol.:  13
  Year:  2010
  Pages:   10.7.3
  Supported by:  IPM
  Abstract:
We generalize well-known Catalan-type integrals for Euler?fs constant to values of the generalized Euler constant function and its derivatives. Using generating functions appearing in these integral representations, we give new Vacca and Ramanujan-type series for values of the generalized Euler constant function and Addison-type series for values of the generalized Euler constant function and its derivative. As a consequence, we get base-B rational series for log [4/(π)], [(G)/(π)] (where G is Catalan's constant), [(ζ′(2))/(π2)] and also for logarithms of the Somos and Glaisher-Kinkelin constants.

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