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DLMF:9.11.E10
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Formula:3615
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MaRDI QID
Q3615
Label: DLMF:9.11.E10
Digital Library of Mathematical Functions ID
9.11.E10
∫
z
w
1
′
w
2
′
d
z
=
3
10
(
-
w
1
w
2
+
z
w
1
w
2
′
+
z
w
1
′
w
2
)
+
1
5
(
z
2
w
1
′
w
2
′
-
z
3
w
1
w
2
)
.
𝑧
subscript
superscript
𝑤
′
1
subscript
superscript
𝑤
′
2
𝑧
3
10
subscript
𝑤
1
subscript
𝑤
2
𝑧
subscript
𝑤
1
subscript
superscript
𝑤
′
2
𝑧
subscript
superscript
𝑤
′
1
subscript
𝑤
2
1
5
superscript
𝑧
2
subscript
superscript
𝑤
′
1
subscript
superscript
𝑤
′
2
superscript
𝑧
3
subscript
𝑤
1
subscript
𝑤
2
{\displaystyle{\displaystyle\int zw^{\prime}_{1}w^{\prime}_{2}\mathrm{d}z=% \tfrac{3}{10}(-w_{1}w_{2}+zw_{1}w^{\prime}_{2}+zw^{\prime}_{1}w_{2})+\tfrac{1}% {5}(z^{2}w^{\prime}_{1}w^{\prime}_{2}-z^{3}w_{1}w_{2}).}}
Constraint(s)
Symbols List
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
: differential of x
∫
{\displaystyle{\displaystyle\int}}
: integral
z
𝑧
{\displaystyle{\displaystyle z}}
: complex variable
w
𝑤
{\displaystyle{\displaystyle w}}
: function
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