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Statements
π
β‘
(
a
,
b
1
2
β’
(
a
+
b
+
1
)
;
z
)
=
(
-
z
β’
(
1
-
z
)
)
(
1
-
a
-
b
)
/
4
β’
P
(
a
-
b
-
1
)
/
2
(
1
-
a
-
b
)
/
2
β‘
(
1
-
2
β’
z
)
,
scaled-hypergeometric-bold-F
π
π
1
2
π
π
1
π§
superscript
π§
1
π§
1
π
π
4
Legendre-P-first-kind
1
π
π
2
π
π
1
2
1
2
π§
{\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop\tfrac{1}{2}(a+b+1)};z%
\right)=\left(-z(1-z)\right)^{\ifrac{(1-a-b)}{4}}\*P^{\ifrac{(1-a-b)}{2}}_{%
\ifrac{(a-b-1)}{2}}\left(1-2z\right),}}
|
ph
β‘
(
-
z
)
|
<
Ο
phase
π§
π
{\displaystyle{\displaystyle\left|\operatorname{ph}\left(-z\right)\right|<\pi}}
P
Ξ½
ΞΌ
β‘
(
z
)
Legendre-P-first-kind
π
π
π§
{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
Ο
{\displaystyle{\displaystyle\pi}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
π
β‘
(
a
,
b
;
c
;
z
)
scaled-hypergeometric-bold-F
π
π
π
π§
{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z%
}\right)}}
z
π§
{\displaystyle{\displaystyle z}}
a
π
{\displaystyle{\displaystyle a}}
b
π
{\displaystyle{\displaystyle b}}
Identifiers
