The Riemann zeta function is defined in the region by the absolutely convergent series Thus, for instance, it is known that , and thus For , the series on the right-hand side of (1) is no longer absolutely convergent, or even conditionally convergent. Nevertheless, the function can be extended to this region (with a pole … Continue reading The Euler-Maclaurin formula, Bernoulli numbers, the zeta function, and real-variable analytic continuation
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