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 2009-02-01, 18:39 #1 mart_r     Dec 2008 you know...around... 929 Posts Zeta(1+s) I can't find anything about it on the web, so I'll post a question here: What is known about the series expansion of Zeta(1+s) when s gets near zero? I found Zeta(1+s) = 1/s + Gamma + s/13.73327... - s²/206.39... - s³/2921.6... + ... (Maybe I have some more questions or results of other calculations of mine I'll post on this thread later on.)
 2009-02-02, 23:26 #2 XYYXF     Jan 2005 Minsk, Belarus 24·52 Posts
 2009-02-03, 17:28 #3 mart_r     Dec 2008 you know...around... 92910 Posts Darn, I really should read more carefully; I've been on this site before. Sorry. Now to something completely different - was someone ever interested in the sum of reciprocals of full reptend primes (http://mathworld.wolfram.com/FullReptendPrime.html)? I figured the sum 1/7+1/17+1/19+... exceeds 1 at about p=10.7*10^9. General formula: Sum(f.r.p.)(1/p) ~ (log log p - 0.4655)*Artin's constant. Any objections? Formulae for bases other than 10?
 2009-02-04, 14:16 #4 XYYXF     Jan 2005 Minsk, Belarus 24·52 Posts Yes, the sum should be Artin*(log log p) + O[1]
2009-02-04, 17:19   #5
mart_r

Dec 2008
you know...around...

929 Posts

Quote:
 Originally Posted by XYYXF Yes, the sum should be Artin*(log log p) + O[1]

I suppose that's equivalent to Artin*(log log p + c) (± prime number irregularities) for some constant c for each base b. At least until I'm more familiar with the niceties of the big-oh notation.

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