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MathGroup Archive 2001

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Non-Integer HarmonicNumbers?

  • To: mathgroup at
  • Subject: [mg29929] Non-Integer HarmonicNumbers?
  • From: Dirk Reiss <reiss at>
  • Date: Thu, 19 Jul 2001 03:56:55 -0400 (EDT)
  • Organization: University of Hamburg -- Germany
  • Sender: owner-wri-mathgroup at


I encountered the combinatorial function HarmonicNumber, which according to the
documentation is defined as a FINITE sum
(It therefore is something one could call an incomplete Zeta function.)
Apart from the definition the documenation does not give much help, e.g.
relations to other special funtions. However, I think there must be some
analytic continuation, since Mathematica is able to compute the the
HarmonicNumber for non-integer values for N, which does not make sense from the
sum definition.

Does anyone know about this, i.e. how does Mathematica compute this Numbers?

Thank you in advance


   Dr. Dirk Reiss
   Institut fuer Laser-Physik     Tel:   (040) 42838-2908
   Universitaet Hamburg           Fax:   (040) 42838-6571
   Jungiusstrasse 9               email: reiss at
   D-20359 Hamburg


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