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Statements
(
1
-
2
x
z
+
z
2
)
-
λ
=
∑
n
=
0
∞
C
n
(
λ
)
(
x
)
z
n
=
∑
n
=
0
∞
(
2
λ
)
n
(
λ
+
1
2
)
n
P
n
(
λ
-
1
2
,
λ
-
1
2
)
(
x
)
z
n
,
superscript
1
2
𝑥
𝑧
superscript
𝑧
2
𝜆
superscript
subscript
𝑛
0
ultraspherical-Gegenbauer-polynomial
𝜆
𝑛
𝑥
superscript
𝑧
𝑛
superscript
subscript
𝑛
0
Pochhammer
2
𝜆
𝑛
Pochhammer
𝜆
1
2
𝑛
Jacobi-polynomial-P
𝜆
1
2
𝜆
1
2
𝑛
𝑥
superscript
𝑧
𝑛
{\displaystyle{\displaystyle(1-2xz+z^{2})^{-\lambda}=\sum_{n=0}^{\infty}C^{(%
\lambda)}_{n}\left(x\right)z^{n}=\sum_{n=0}^{\infty}\frac{{\left(2\lambda%
\right)_{n}}}{{\left(\lambda+\tfrac{1}{2}\right)_{n}}}P^{(\lambda-\frac{1}{2},%
\lambda-\frac{1}{2})}_{n}\left(x\right)z^{n},}}
|
z
|
<
1
𝑧
1
{\displaystyle{\displaystyle|z|<1}}
P
n
(
α
,
β
)
(
x
)
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑥
{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(%
\NVar{x}\right)}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
C
n
(
λ
)
(
x
)
ultraspherical-Gegenbauer-polynomial
𝜆
𝑛
𝑥
{\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}%
\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
