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