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Recurrence and Sum Functions
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Built-in
Mathematica
Symbol
Combinatorial Functions
Tutorials »
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EulerGamma
PolyGamma
Zeta
Log
HarmonicMean
ZipfDistribution
See Also »
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Discrete Calculus
Integer Functions
Recurrence and Sum Functions
More About »
HarmonicNumber
HarmonicNumber
[
n
]
gives the
n
harmonic number
.
HarmonicNumber
[
n
,
r
]
gives the harmonic number
of order
r
.
MORE INFORMATION
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
CLOSE ALL
Basic Examples
(3)
First ten harmonic numbers:
In[1]:=
Out[1]=
Plot harmonic numbers:
In[1]:=
Out[1]=
Carry out sums involving harmonic numbers:
In[1]:=
Out[1]=
Scope
(8)
Generalizations & Extensions
(5)
Applications
(4)
Properties & Relations
(5)
Possible Issues
(3)
SEE ALSO
EulerGamma
PolyGamma
Zeta
Log
HarmonicMean
ZipfDistribution
TUTORIALS
Combinatorial Functions
RELATED LINKS
MathWorld
The Wolfram Functions Site
MORE ABOUT
Discrete Calculus
Integer Functions
Recurrence and Sum Functions
New in 4
harmonic number 
. 
of order r. 
with 
.
EXAMPLES
Basic Examples 
Scope 