## “School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

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.

Download TeX format
back to top
scroll left or right