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

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]=

Listable | NumericFunction | Protected | ReadProtected

Gamma | LogGamma | EulerGamma | HarmonicNumber | QPolyGamma | HurwitzZeta

489th most common (1 in 23700 symbols)

1395th most common (1 in 924000 symbols)

1106th most common (1 in 21500 symbols)

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