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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




Re: Is there a continuous function that maps to the harmonic series at the integers?
Posted:
Aug 2, 2011 8:37 PM


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 EulerMascheoni 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 to view any ASCII art, display article in a monospaced font



