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2009-02-01, 18:39
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#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.) |
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2009-02-02, 23:26
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#2 |
Jan 2005
Minsk, Belarus
24·52 Posts |
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2009-02-03, 17:28
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#3 |
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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? |
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2009-02-04, 14:16
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#4 |
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Jan 2005
Minsk, Belarus
24·52 Posts |
Yes, the sum should be
Artin*(log log p) + O[1] |
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2009-02-04, 17:19
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#5 | |
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Dec 2008
you know...around...
929 Posts |
Quote:
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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