PolyGamma

PolyGamma[z]

gives the digamma function .

PolyGamma[n,z]

gives the n^(th) derivative of the digamma function .

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • PolyGamma[z] is the logarithmic derivative of the gamma function, given by .
  • PolyGamma[n,z] is given for positive integer by .
  • For arbitrary complex n, the polygamma function is defined by fractional calculus analytic continuation.
  • PolyGamma[z] and PolyGamma[n,z] are meromorphic functions of z with no branch cut discontinuities.
  • For certain special arguments, PolyGamma automatically evaluates to exact values.
  • PolyGamma can be evaluated to arbitrary numerical precision.
  • PolyGamma automatically threads over lists.

Examples

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Basic Examples  (3)

Evaluate the digamma function:

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Evaluate quadrogamma:

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Derivative of the gamma function:

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The digamma function:

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Scope  (9)

Generalizations & Extensions  (8)

Applications  (3)

Properties & Relations  (9)

Possible Issues  (3)

See Also

Gamma  LogGamma  EulerGamma  HarmonicNumber  QPolyGamma

Tutorials

Introduced in 1988
(1.0)
| Updated in 2007
(6.0)