### 5.9.9 Derivatives of the DiGamma function : Psi

Psi takes as arguments a real a and an integer n (by default n=0).
Psi returns the value of the n-th derivative of the DiGamma function at x=a, where the DiGamma function is the first derivative of ln(Γ(x)). This function is used to evaluated sums of rational functions having poles at integers.
Input :

Psi(3,1)

Output :

pi`^`2/6-5/4

If n=0, you may use Psi(a) instead of Psi(a,0) to compute the value of the DiGamma function at x=a.
Input :

Psi(3)

Output :

Psi(1)+3/2

Input :

evalf(Psi(3))

Output :

.922784335098