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2.11.E13 - MaRDI portal
Statements
F
n
+
p
(
z
)
∼
e
-
i
(
ρ
+
α
)
θ
1
+
e
-
i
θ
e
-
ρ
-
z
(
2
π
ρ
)
1
/
2
∑
s
=
0
∞
a
2
s
(
θ
,
α
)
ρ
s
,
asymptotic-expansion
terminant-function
𝑛
𝑝
𝑧
superscript
𝑒
𝑖
𝜌
𝛼
𝜃
1
superscript
𝑒
𝑖
𝜃
superscript
𝑒
𝜌
𝑧
superscript
2
𝜋
𝜌
1
2
superscript
subscript
𝑠
0
subscript
𝑎
2
𝑠
𝜃
𝛼
superscript
𝜌
𝑠
{\displaystyle{\displaystyle F_{n+p}\left(z\right)\sim\frac{e^{-i(\rho+\alpha)%
\theta}}{1+e^{-i\theta}}\frac{e^{-\rho-z}}{(2\pi\rho)^{1/2}}\sum_{s=0}^{\infty%
}\frac{a_{2s}(\theta,\alpha)}{\rho^{s}},}}
ρ
→
∞
→
𝜌
{\displaystyle{\displaystyle\rho\to\infty}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
F
p
(
z
)
terminant-function
𝑝
𝑧
{\displaystyle{\displaystyle F_{\NVar{p}}\left(\NVar{z}\right)}}
ρ
𝜌
{\displaystyle{\displaystyle\rho}}
θ
𝜃
{\displaystyle{\displaystyle\theta}}
a
2
s
(
θ
,
α
)
subscript
𝑎
2
𝑠
𝜃
𝛼
{\displaystyle{\displaystyle a_{2s}(\theta,\alpha)}}
Identifiers