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Are there variations of Ramaswami's formula for the analytic continuation of the Riemann zeta function?

On p. 286 of Borwein's paper entitled "Computational Strategies for the Riemann zeta function", the author mentions a formula due to Ramaswami: $$(1-2^{1-s})\zeta(s) = \sum_{n=1}^{\infty} \...
Max Lonysa Muller's user avatar