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DLMF:23.6.E34
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Formula:7970
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MaRDI QID
Q7970
Label: DLMF:23.6.E34
Digital Library of Mathematical Functions ID
23.6.E34
2
ω
1
=
∫
e
1
∞
d
u
(
u
-
e
1
)
(
u
-
e
2
)
(
u
-
e
3
)
=
∫
e
3
e
2
d
u
(
e
1
-
u
)
(
e
2
-
u
)
(
u
-
e
3
)
,
2
subscript
𝜔
1
superscript
subscript
Weierstrass-e-on-lattice
1
𝕃
𝑢
𝑢
Weierstrass-e-on-lattice
1
𝕃
𝑢
Weierstrass-e-on-lattice
2
𝕃
𝑢
Weierstrass-e-on-lattice
3
𝕃
superscript
subscript
Weierstrass-e-on-lattice
3
𝕃
Weierstrass-e-on-lattice
2
𝕃
𝑢
Weierstrass-e-on-lattice
1
𝕃
𝑢
Weierstrass-e-on-lattice
2
𝕃
𝑢
𝑢
Weierstrass-e-on-lattice
3
𝕃
{\displaystyle{\displaystyle 2\omega_{1}=\int_{e_{1}}^{\infty}\frac{\mathrm{d}% u}{\sqrt{(u-e_{1})(u-e_{2})(u-e_{3})}}=\int_{e_{3}}^{e_{2}}\frac{\mathrm{d}u}{% \sqrt{(e_{1}-u)(e_{2}-u)(u-e_{3})}},}}
Constraint(s)
Symbols List
e
j
Weierstrass-e-on-lattice
𝑗
𝕃
{\displaystyle{\displaystyle e_{\NVar{j}}}}
:
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
: differential of x
∫
{\displaystyle{\displaystyle\int}}
: integral
𝕃
𝕃
{\displaystyle{\displaystyle\mathbb{L}}}
: lattice
ω
1
subscript
𝜔
1
{\displaystyle{\displaystyle\omega_{1}}}
: lattice generators
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