We have different summation senses under which Cauchy-divergent series can be summed to finite values. I was wondering if such a procedure existed for the Harmonic series, [itex]\sum_{n = 1}^{\infty} n^{-1}[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

I'm putting this in the number theory discussion since the obvious connection with the Riemann zeta-function's pole at unity. However this guarantees there's no basic zeta regularization to the harmonic- so is there a deeper zeta-based result? Or some other way in which a value might be assigned to it? (the only one I know of is the Ramanujan sum of [itex]\gamma[/tex], which is just based on the definition of Euler's constant in the case of the harmonic- and expressing this in terms of other constants has so far proven futile)

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# Resummation of the Harmonic series!

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