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DLMF:19.11.E5 - MaRDI portal
Statements
Π
(
θ
,
α
2
,
k
)
+
Π
(
ϕ
,
α
2
,
k
)
=
Π
(
ψ
,
α
2
,
k
)
-
α
2
R
C
(
γ
-
δ
,
γ
)
,
elliptic-integral-third-kind-Pi
𝜃
superscript
𝛼
2
𝑘
elliptic-integral-third-kind-Pi
italic-ϕ
superscript
𝛼
2
𝑘
elliptic-integral-third-kind-Pi
𝜓
superscript
𝛼
2
𝑘
superscript
𝛼
2
Carlson-integral-RC
𝛾
𝛿
𝛾
{\displaystyle{\displaystyle\Pi\left(\theta,\alpha^{2},k\right)+\Pi\left(\phi,%
\alpha^{2},k\right)=\Pi\left(\psi,\alpha^{2},k\right)-\alpha^{2}R_{C}\left(%
\gamma-\delta,\gamma\right),}}
R
C
(
x
,
y
)
Carlson-integral-RC
𝑥
𝑦
{\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
Π
(
ϕ
,
α
2
,
k
)
elliptic-integral-third-kind-Pi
italic-ϕ
superscript
𝛼
2
𝑘
{\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}%
\right)}}
ϕ
italic-ϕ
{\displaystyle{\displaystyle\phi}}
k
𝑘
{\displaystyle{\displaystyle k}}
α
2
superscript
𝛼
2
{\displaystyle{\displaystyle\alpha^{2}}}
θ
𝜃
{\displaystyle{\displaystyle\theta}}
ψ
𝜓
{\displaystyle{\displaystyle\psi}}
γ
𝛾
{\displaystyle{\displaystyle\gamma}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
Identifiers