PolyGamma(n, z)
n
n can be any integer >= -1
When n==-1 the LnGamma(z) function is returned.
When n==0 the DiGamma(z) or Psi(z) function is returned.
When n>0 the (n+1) derivative of the Logarithm of the Gamma(z) function is returned.

z
Real or complex number.

Description
Returns the PolyGamma function.

Examples
PolyGamma(0, z)
Psi
(
z
)
PolyGamma(-1, z)
ln
(
Gamma
(
z
)
)
PolyGamma(2, 2.5)
-0.2362040516417274
PolyGamma(3, -1/3)
63014578
121807
PolyGamma(4, 3z)
1
243
PolyGamma
(
4
,
z
)
+
1
243
PolyGamma
4
,
z
+
1
3
+
1
243
PolyGamma
4
,
z
+
2
3
PolyGamma(2, z+3)
2
z
3
+
2
(
z
+
1
)
3
+
2
(
z
+
2
)
3
+
PolyGamma
(
2
,
z
)
Diff(PolyGamma(n, z), z)
PolyGamma
(
n
+
1
,
z
)
Solve(PolyGamma(1, x)=5)
[
0.4961687347040657
,
...
]
Solve(PolyGamma(2, x)=10, x, [-1, 0])
-0.4461094043583577
Plot(PolyGamma(1, x), x=[-10, 10], y=[0, 20])
-12-8-40481224201612840
Plot(PolyGamma(2, x), x=[-5, 5], y=[-5, 5])
-6-4-202466420-2-4-6

References

Related Functions
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
Q
R
S
T
V
W
Z