This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)
 Documentation / Mathematica / Built-in Functions / Mathematical Functions / Factorial Related  /
PolyGamma

  • PolyGamma[ z ] gives the digamma function .
  • PolyGamma[ n , z ] gives derivative of the digamma function .
  • PolyGamma[ z ] is the logarithmic derivative of the gamma function, given by .
  • PolyGamma[ n , z ] is given by .
  • The digamma function is ; is the logarithmic derivative of the gamma function.
  • PolyGamma[ z ] and PolyGamma[ n , z ] are entire functions of z with no branch cut discontinuities.
  • See the Mathematica book: Section 3.2.10.
  • See also Implementation NotesA.9.44.15MainBookLinkOldButtonDataA.9.44.15.
  • See also: Gamma, LogGamma, EulerGamma.

    Further Examples

    This is the derivative.

    In[1]:=

    Out[1]=

    This is the integral.

    In[2]:=

    Out[2]=

    PolyGamma[x] satisfies its defining identity.

    In[3]:=

    Out[3]=

    This is a series expansion around .

    In[4]:=

    Out[4]=