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Polygamma Function

Usage

PolyGamma[z] gives the digamma function ψ (z).
PolyGamma[n, z] gives the n ^th derivative of the digamma function ψ^(n) (z).

Basic examples

$Evaluate the digamma function: In[1]:=PolyGamma[5] Out[1]=25/12 - EulerGamma Evaluate the pentagamma function: In[2]:=PolyGamma[3, 5] Out[2]=6 (-22369/20736 + π^4/90) Evaluate the second derivative of the gamma function: In[1]:=D[Gamma[z], {z, 2}] Out[1]=Gamma[z] (PolyGamma[0, z])^2 + Gamma[z] PolyGamma[1, z] Plot the digamma function over a subset of the reals: In[1]:=Plot[PolyGamma[x], {x, -3, 3}] Out[1]=$

Attributes

Listable | NumericFunction | Protected | ReadProtected

Relationships with other entities

Relationships with other entities

Typical ranks of usage in programs

489th most common (1 in 23700 symbols)

1395th most common (1 in 924000 symbols)

1106th most common (1 in 21500 symbols)

History

introduced in Version 1 (June 1988)
last modified in Version 13.1 (June 2022)

Timeline

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