DLMF:19.14.E1 (Q6306): Difference between revisions

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Property / constraint
 

k 2 = 2 - 3 4 superscript 𝑘 2 2 3 4 {\displaystyle{\displaystyle k^{2}=\dfrac{2-\sqrt{3}}{4}}}

k^{2}=\dfrac{2-\sqrt{3}}{4}
Property / constraint: k 2 = 2 - 3 4 superscript 𝑘 2 2 3 4 {\displaystyle{\displaystyle k^{2}=\dfrac{2-\sqrt{3}}{4}}} / rank
 
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Revision as of 17:06, 30 December 2019

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DLMF:19.14.E1
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    1 x d t t 3 - 1 = 3 - 1 / 4 F ( ϕ , k ) , superscript subscript 1 𝑥 𝑡 superscript 𝑡 3 1 superscript 3 1 4 elliptic-integral-first-kind-F italic-ϕ 𝑘 {\displaystyle{\displaystyle\int_{1}^{x}\frac{\mathrm{d}t}{\sqrt{t^{3}-1}}=3^{% -1/4}F\left(\phi,k\right),}}
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    cos ϕ = 3 + 1 - x 3 - 1 + x italic-ϕ 3 1 𝑥 3 1 𝑥 {\displaystyle{\displaystyle\cos\phi=\dfrac{\sqrt{3}+1-x}{\sqrt{3}-1+x}}}
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    cos ϕ = 3 + 1 - x 3 - 1 + x italic-ϕ 3 1 𝑥 3 1 𝑥 {\displaystyle{\displaystyle\cos\phi=\dfrac{\sqrt{3}+1-x}{\sqrt{3}-1+x}}}
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    k 2 = 2 - 3 4 superscript 𝑘 2 2 3 4 {\displaystyle{\displaystyle k^{2}=\dfrac{2-\sqrt{3}}{4}}}
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