DLMF:19.14.E3 (Q6308)

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Language	Label	Description	Also known as
English	DLMF:19.14.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{x}\frac{\mathrm{d}t}{\sqrt{1+t^{4}}}=% \frac{\operatorname{sign}\left(x\right)}{2}F\left(\phi,k\right),}}

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DLMF:19.14.E3

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{\displaystyle{\displaystyle\cos\phi=\dfrac{1-x^{2}}{1+x^{2}}}}

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{\displaystyle{\displaystyle\cos\phi=\dfrac{1-x^{2}}{1+x^{2}}}}

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{\displaystyle{\displaystyle k^{2}=\dfrac{1}{2}}}

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1abdec

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Legendre’s incomplete elliptic integral of the first kind

Defining formula

{\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}

C19.S2.E4.m2abdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}

introduction.Sx4.p2.t1.r18.m6adec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1bdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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