Author(s):
1. Lubomir Markov:
Department of Mathematics and Computer Science, Barry University,Miami Shores, Florida 33161,USA
Abstract:
The series P1k=0 GN(k) (2k+1)r and P1 k=1 HN(k) kr are considered, where GN(k) and HN(k) are the Borwein-Chamberland sums appeared in the expansions of integer powers of the arcsine reported in the paper [D. Borwein, M. Chamberland, Int. J. Math. Math. Sci. 2007 (2007) #1981]. For 3 _ r 2 N; representations for these series in terms of zeta values are derived, extending a theorem proved in the paper [J. Ewell, Canad. Math. Bull. 34 (1991) 60-66]. Several corollaries (especially for the case r = 3) are obtained, extending some known representations, including Euler’s famous rapidly converging series for _(3). The technique can be applied to the case r = 2 and it yields generalizations of the formulas P1 k=0 1 (2k+1)2 = _2 8 and P1 k=1 1 k2 = _2 6 :
Page(s):
138-144
Published:
Journal: Discrete Mathematics Letters, Volume: 12, Issue: 0, Year: 2023
Keywords:
BorweinChamberland sums
,
BorweinChamberland expansions
,
Ewells theorem
,
Euler sums
,
Eulers series for 3
References:
References are not available for this document.
Citations
Citations are not available for this document.