DLMF:19.6#Ex5
(Q6145)
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English
DLMF:19.6#Ex5
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Statements
Defining formula
Π
(
-
k
,
k
)
=
1
4
π
(
1
+
k
)
-
1
+
1
2
K
(
k
)
,
complete-elliptic-integral-third-kind-Pi
𝑘
𝑘
1
4
𝜋
superscript
1
𝑘
1
1
2
complete-elliptic-integral-first-kind-K
𝑘
{\displaystyle{\displaystyle\Pi\left(-k,k\right)=\tfrac{1}{4}\pi(1+k)^{-1}+% \tfrac{1}{2}K\left(k\right),}}
0 references
DLMF id
DLMF:19.6#Ex5
0 references
constraint
0
≤
k
2
<
1
0
superscript
𝑘
2
1
{\displaystyle{\displaystyle 0\leq k^{2}<1}}
0 references
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