20090201, 18:39  #1 
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.) 
20090202, 23:26  #2 
Jan 2005
Minsk, Belarus
2^{4}·5^{2} Posts 

20090203, 17:28  #3 
Dec 2008
you know...around...
929_{10} 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? 
20090204, 14:16  #4 
Jan 2005
Minsk, Belarus
2^{4}·5^{2} Posts 
Yes, the sum should be
Artin*(log log p) + O[1] 
20090204, 17:19  #5 
Dec 2008
you know...around...
929 Posts 

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