Derivatives of the DiGamma function

The DiGamma function is the derivative of the logarithm of the Γ function (see Section 7.3.13),

ψ(z)=

ln(Γ(z))=

Γ′(z)

Γ(z)

This function is used to evaluated sums of rational functions having poles at integers.

The Psi function computes the DiGamma function and its derivatives.

Psi takes one mandatory argument and one optional argument:
- a, a real number.
- Optionally, n, a non-negative integer.
Psi(a) returns the value of the DiGamma function ψ(a).
Psi(a,n) returns the nth derivative of the DiGamma function at x=a.

Psi(3)

−γ

evalf(Psi(3))

0.922784335098

Psi(3,1)

π ²

−