High Quality Content by WIKIPEDIA articles! In mathematics, a zeta constant is a number obtained by plugging an integer into the Riemann zeta function. This article provides a number of series identities for the zeta function for integer values. It is known that ?(3) is irrational (Apery's theorem) and that infinitely many of the numbers ?(2n+1) (n ? N) are irrational. There are also results on the (ir)rationality of values of the Riemann zeta function at the elements of certain subsets of the positive odd integers; for example, at least one of ?(5), ?(7), ?(9), or ?(11) is irrational. Most of the identities following below are provided by Simon Plouffe. They are notable in that they converge quite rapidly, giving almost three digits of precision per iteration, and are thus useful for high-precision calculations.

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