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DLMF:10.17.E17 - MaRDI portal
Statements
R
ℓ
±
(
ν
,
z
)
=
(
-
1
)
ℓ
2
cos
(
ν
π
)
(
∑
k
=
0
m
-
1
(
±
i
)
k
a
k
(
ν
)
z
k
G
ℓ
-
k
(
∓
2
i
z
)
+
R
m
,
ℓ
±
(
ν
,
z
)
)
,
superscript
subscript
𝑅
ℓ
plus-or-minus
𝜈
𝑧
superscript
1
ℓ
2
𝜈
𝜋
superscript
subscript
𝑘
0
𝑚
1
superscript
plus-or-minus
𝑖
𝑘
subscript
𝑎
𝑘
𝜈
superscript
𝑧
𝑘
rescaled-terminant-function
ℓ
𝑘
minus-or-plus
2
𝑖
𝑧
superscript
subscript
𝑅
𝑚
ℓ
plus-or-minus
𝜈
𝑧
{\displaystyle{\displaystyle R_{\ell}^{\pm}(\nu,z)=(-1)^{\ell}2\cos\left(\nu%
\pi\right)\*\left(\sum_{k=0}^{m-1}(\pm i)^{k}\frac{a_{k}(\nu)}{z^{k}}G_{\ell-k%
}\left(\mp 2iz\right)+R_{m,\ell}^{\pm}(\nu,z)\right),}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
G
p
(
z
)
rescaled-terminant-function
𝑝
𝑧
{\displaystyle{\displaystyle G_{\NVar{p}}\left(\NVar{z}\right)}}
m
𝑚
{\displaystyle{\displaystyle m}}
k
𝑘
{\displaystyle{\displaystyle k}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
a
k
(
ν
)
subscript
𝑎
𝑘
𝜈
{\displaystyle{\displaystyle a_{k}(\nu)}}
R
ℓ
±
(
ν
,
z
)
superscript
subscript
𝑅
ℓ
plus-or-minus
𝜈
𝑧
{\displaystyle{\displaystyle R_{\ell}^{\pm}(\nu,z)}}
Identifiers