Open Access
2014 Rapidly Converging Series for ζ(2n+1) from Fourier Series
Junesang Choi
Abstr. Appl. Anal. 2014(SI30): 1-9 (2014). DOI: 10.1155/2014/457620


Ever since Euler first evaluated ζ(2) and ζ(2m), numerous interesting solutions of the problem of evaluating the ζ(2m) (m) have appeared in the mathematical literature. Until now no simple formula analogous to the evaluation of ζ(2m) (m) is known for ζ(2m+1) (m) or even for any special case such as ζ(3). Instead, various rapidly converging series for ζ(2m+1) have been developed by many authors. Here, using Fourier series, we aim mainly at presenting a recurrence formula for rapidly converging series for ζ(2m+1). In addition, using Fourier series and recalling some indefinite integral formulas, we also give recurrence formulas for evaluations of β(2m+1) and ζ(2m) (m), which have been treated in earlier works.


Download Citation

Junesang Choi. "Rapidly Converging Series for ζ(2n+1) from Fourier Series." Abstr. Appl. Anal. 2014 (SI30) 1 - 9, 2014.


Published: 2014
First available in Project Euclid: 26 March 2014

MathSciNet: MR3166615
Digital Object Identifier: 10.1155/2014/457620

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI30 • 2014
Back to Top