LegendreP(n, z)
n
Positive integer.

z
Real or complex number.

Description
Returns the Legendre polynomial or Legendre function of the first kind.

Examples
LegendreP(n, 0)
2
π
n
Gamma
n
2
Gamma
-
n
+
1
2
LegendreP(n, 1)
1
LegendreP(0, z)
1
LegendreP(1, z)
z
LegendreP(7, z)
429
z
7
16
-
693
z
5
16
+
315
z
3
16
-
35
z
16
LegendreP(7, 1/2)
457
2048
LegendreP(7, -1/2z)
-
429
z
7
2048
+
693
z
5
512
-
315
z
3
128
+
35
z
32
LegendreP(4, z+1/2)
35
z
4
8
+
35
z
3
4
+
45
z
2
16
-
25
z
16
-
37
128

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