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Statements
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superscript
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2
1
𝑥
𝑧
1
2
𝛼
Bessel-J
𝛼
2
1
𝑥
𝑧
superscript
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2
1
𝑥
𝑧
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2
𝛽
modified-Bessel-first-kind
𝛽
2
1
𝑥
𝑧
superscript
subscript
𝑛
0
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑥
Euler-Gamma
𝑛
𝛼
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Euler-Gamma
𝑛
𝛽
1
superscript
𝑧
𝑛
{\displaystyle{\displaystyle\left(\tfrac{1}{2}(1-x)z\right)^{-\frac{1}{2}%
\alpha}J_{\alpha}\left(\sqrt{2(1-x)z}\right)\*\left(\tfrac{1}{2}(1+x)z\right)^%
{-\frac{1}{2}\beta}I_{\beta}\left(\sqrt{2(1+x)z}\right)=\sum_{n=0}^{\infty}%
\frac{P^{(\alpha,\beta)}_{n}\left(x\right)}{\Gamma\left(n+\alpha+1\right)%
\Gamma\left(n+\beta+1\right)}z^{n}.}}
J
ν
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z
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Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
Γ
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z
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Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
P
n
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α
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β
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x
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Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑥
{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(%
\NVar{x}\right)}}
I
ν
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z
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modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
