EllipticPi
Elliptic Integrals
EllipticPi[
n
,
z
,
m
]
Series representations
Generalized power series
Expansions on branch cuts
Formulas on real axis for real
m
,
n
(36 formulas)
For
m
<1<
n
,csc
-1
(
n
1/2
)+Pi
u
<
x
u+1/2)/;
u
∈
Z
(3 formulas)
For
m
<1<
n
,Pi(
u
+1/2)<
x
u+1)-csc
-1
(
n
1/2
)/;
u
∈
Z
(3 formulas)
For
n
<1<
m
,csc
-1
(
m
1/2
)+Pi
u
<
x
u+1/2)/;
u
∈
Z
(3 formulas)
For
n
<1<
m
,Pi(
u
+1/2)<
x
u+1)-csc
-1
(
m
1/2
)/;
u
∈
Z
(3 formulas)
For 1<
n
<
m
,csc
-1
(
m
1/2
)+Pi
u
<
x
u+1/2)/;
u
∈
Z
(6 formulas)
For 1<
n
<
m
,Pi(
u
+1/2)<
x
u+1)-csc
-1
(
m
1/2
)/;
u
∈
Z
(6 formulas)
For 1<
m
<
n
,csc
-1
(
n
1/2
)+Pi
u
<
x
u+1/2)/;
u
∈
Z
(6 formulas)
For 1<
m
<
n
,Pi(
u
+1/2)<
x
u+1)-csc
-1
(
n
1/2
)/;
u
∈
Z
(6 formulas)
EllipticPi[
n
,
m
]