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DLMF:36.10.E2 - MaRDI portal
Statements
∂
K
+
1
Ψ
K
(
𝐱
)
∂
x
1
K
+
1
+
∑
m
=
1
K
(
-
i
)
m
-
K
-
2
(
m
x
m
K
+
2
)
∂
m
-
1
Ψ
K
(
𝐱
)
∂
x
1
m
-
1
=
0
.
partial-derivative
canonical-integral
𝐾
𝐱
subscript
𝑥
1
𝐾
1
superscript
subscript
𝑚
1
𝐾
superscript
𝑖
𝑚
𝐾
2
𝑚
subscript
𝑥
𝑚
𝐾
2
partial-derivative
canonical-integral
𝐾
𝐱
subscript
𝑥
1
𝑚
1
0
{\displaystyle{\displaystyle\frac{{\partial}^{K+1}\Psi_{K}\left(\mathbf{x}%
\right)}{{\partial x_{1}}^{K+1}}+\sum_{m=1}^{K}(-i)^{m-K-2}\left(\frac{mx_{m}}%
{K+2}\right)\frac{{\partial}^{m-1}\Psi_{K}\left(\mathbf{x}\right)}{{\partial x%
_{1}}^{m-1}}=0.}}
Ψ
K
(
𝐱
)
canonical-integral
𝐾
𝐱
{\displaystyle{\displaystyle\Psi_{\NVar{K}}\left(\NVar{\mathbf{x}}\right)}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∂
f
∂
x
partial-derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
∂
x
𝑥
{\displaystyle{\displaystyle\partial\NVar{x}}}
n
𝑛
{\displaystyle{\displaystyle n}}
K
𝐾
{\displaystyle{\displaystyle K}}
x
i
subscript
𝑥
𝑖
{\displaystyle{\displaystyle x_{i}}}
Identifiers