HarmonicNumber

HarmonicNumber[n]

gives the n^(th) harmonic number .

HarmonicNumber[n,r]

gives the harmonic number of order r.

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The harmonic numbers are given by with .
  • HarmonicNumber can be evaluated to arbitrary numerical precision.
  • HarmonicNumber automatically threads over lists.

Examples

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Basic Examples  (3)

First ten harmonic numbers:

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Plot harmonic numbers:

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Carry out sums involving harmonic numbers:

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Scope  (8)

Generalizations & Extensions  (5)

Applications  (4)

Properties & Relations  (9)

Possible Issues  (3)

See Also

EulerGamma  PolyGamma  Zeta  Log  HarmonicMean  ZipfDistribution

Tutorials

Introduced in 1999
(4.0)