Ever since Euler first evaluated and , numerous interesting solutions of the problem of evaluating the have appeared in the mathematical literature. Until now no simple formula analogous to the evaluation of is known for or even for any special case such as . Instead, various rapidly converging series for have been developed by many authors. Here, using Fourier series, we aim mainly at presenting a recurrence formula for rapidly converging series for . In addition, using Fourier series and recalling some indefinite integral formulas, we also give recurrence formulas for evaluations of and , which have been treated in earlier works.
Junesang Choi. "Rapidly Converging Series for from Fourier Series." Abstr. Appl. Anal. 2014 (SI30) 1 - 9, 2014. https://doi.org/10.1155/2014/457620