6.8.17 Derivatives of the DiGamma function: Psi
The DiGamma function is the derivative of the logarithm of the
Γ function (see Section 6.8.13),
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.
Examples.
-
Input:
Psi(3)
Output:
- Input:
evalf(Psi(3))
Output:
- Input:
Psi(3,1)
Output: