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Topic: Is there a continuous function that maps to the harmonic series at
the integers?

Replies: 3   Last Post: Aug 2, 2011 8:37 PM

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Rob Johnson

Posts: 1,771
Registered: 12/6/04
Re: Is there a continuous function that maps to the harmonic series at the integers?
Posted: Aug 2, 2011 8:37 PM
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In article <4E35AB1E.5070700@netscape.net>,
"Stephen J. Herschkorn" <sjherschko@netscape.net> wrote:
>G.Waleed Kavalec wrote:
>

>>Question: Is there a continuous function that maps to the harmonic
>>series at the integers?
>>
>>Given that for x at integer n, y = sum (1 ... 1/n).
>>
>>Is there a smooth continuous f(x) that is equivalent?
>>
>>

>"H_n = g + f(n+1), where g is the Euler-Mascheoni constant and f is
>the digama function.."
>
>http://mathworld.wolfram.com/HarmonicNumber.html (which uses themore
>usual Greek charactters in place of "g" and "f")


This function can also be obtained as

+oo
--- 1 1
H(n) = > ( - - --- )
--- k k+n
k=1

which converges absolutely for all complex n.

Rob Johnson <rob@trash.whim.org>
take out the trash before replying
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