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Statements
R
-
a
(
b
1
,
…
,
b
4
;
c
-
1
,
c
-
k
2
,
c
,
c
-
α
2
)
=
2
(
sin
2
ϕ
)
1
-
a
′
B
(
a
,
a
′
)
∫
0
ϕ
(
sin
θ
)
2
a
-
1
(
sin
2
ϕ
-
sin
2
θ
)
a
′
-
1
(
cos
θ
)
1
-
2
b
1
(
1
-
k
2
sin
2
θ
)
-
b
2
(
1
-
α
2
sin
2
θ
)
-
b
4
d
θ
,
Carlson-integral-R
𝑎
subscript
𝑏
1
…
subscript
𝑏
4
𝑐
1
𝑐
superscript
𝑘
2
𝑐
𝑐
superscript
𝛼
2
2
superscript
2
italic-ϕ
1
superscript
𝑎
′
Euler-Beta
𝑎
superscript
𝑎
′
superscript
subscript
0
italic-ϕ
superscript
𝜃
2
𝑎
1
superscript
2
italic-ϕ
2
𝜃
superscript
𝑎
′
1
superscript
𝜃
1
2
subscript
𝑏
1
superscript
1
superscript
𝑘
2
2
𝜃
subscript
𝑏
2
superscript
1
superscript
𝛼
2
2
𝜃
subscript
𝑏
4
𝜃
{\displaystyle{\displaystyle R_{-a}\left(b_{1},\dots,b_{4};c-1,c-k^{2},c,c-%
\alpha^{2}\right)=\frac{2({\sin^{2}}\phi)^{1-a^{\prime}}}{\mathrm{B}\left(a,a^%
{\prime}\right)}\int_{0}^{\phi}(\sin\theta)^{2a-1}{({\sin^{2}}\phi-{\sin^{2}}%
\theta)}^{a^{\prime}-1}\*(\cos\theta)^{1-2b_{1}}{(1-k^{2}{\sin^{2}}\theta)}^{-%
b_{2}}{(1-\alpha^{2}{\sin^{2}}\theta)}^{-b_{4}}\mathrm{d}\theta,}}
R
-
a
(
b
1
,
…
,
b
n
;
z
1
,
…
,
z
n
)
Carlson-integral-R
𝑎
subscript
𝑏
1
…
subscript
𝑏
𝑛
subscript
𝑧
1
…
subscript
𝑧
𝑛
{\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}%
};\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}
B
(
a
,
b
)
Euler-Beta
𝑎
𝑏
{\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
ϕ
italic-ϕ
{\displaystyle{\displaystyle\phi}}
k
𝑘
{\displaystyle{\displaystyle k}}
α
2
superscript
𝛼
2
{\displaystyle{\displaystyle\alpha^{2}}}
Identifiers
