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DLMF:31.10.E19 - MaRDI portal
Statements
𝒦
(
u
,
v
,
w
)
=
u
1
-
γ
v
1
-
δ
w
1
-
ϵ
𝒞
1
-
γ
(
u
σ
1
)
𝒞
1
-
δ
(
v
σ
2
)
𝒞
1
-
ϵ
(
i
w
σ
1
+
σ
2
)
,
𝒦
𝑢
𝑣
𝑤
superscript
𝑢
1
𝛾
superscript
𝑣
1
𝛿
superscript
𝑤
1
italic-ϵ
cylinder-function
1
𝛾
𝑢
subscript
𝜎
1
cylinder-function
1
𝛿
𝑣
subscript
𝜎
2
cylinder-function
1
italic-ϵ
imaginary-unit
𝑤
subscript
𝜎
1
subscript
𝜎
2
{\displaystyle{\displaystyle\mathcal{K}(u,v,w)=u^{1-\gamma}v^{1-\delta}w^{1-%
\epsilon}\mathscr{C}_{1-\gamma}\left(u\sqrt{\sigma_{1}}\right)\*\mathscr{C}_{1%
-\delta}\left(v\sqrt{\sigma_{2}}\right)\mathscr{C}_{1-\epsilon}\left(\mathrm{i%
}w\sqrt{\sigma_{1}+\sigma_{2}}\right),}}
𝒞
ν
(
z
)
cylinder-function
𝜈
𝑧
{\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
γ
𝛾
{\displaystyle{\displaystyle\gamma}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
ϵ
italic-ϵ
{\displaystyle{\displaystyle\epsilon}}
𝒦
(
z
;
s
,
t
)
𝒦
𝑧
𝑠
𝑡
{\displaystyle{\displaystyle\mathcal{K}(z;s,t)}}
u
𝑢
{\displaystyle{\displaystyle u}}
v
𝑣
{\displaystyle{\displaystyle v}}
w
𝑤
{\displaystyle{\displaystyle w}}
σ
1
subscript
𝜎
1
{\displaystyle{\displaystyle\sigma_{1}}}
Identifiers