DLMF:19.2.E16 (Q6112)

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Language	Label	Description	Also known as
English	DLMF:19.2.E16	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{el3}\left(x,k_{c},p\right)=\int_{0}^{% \operatorname{arctan}x}\frac{\mathrm{d}\theta}{({\cos^{2}}\theta+p{\sin^{2}}% \theta)\sqrt{{\cos^{2}}\theta+k_{c}^{2}{\sin^{2}}\theta}}=\Pi\left(% \operatorname{arctan}x,1-p,k\right),}}

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DLMF:19.2.E16

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Symbols defined

Bulirsch’s incomplete elliptic integral of the third kind

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{\displaystyle{\displaystyle x^{2}\neq-1/p}}

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cosine function

Defining formula

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

C4.S14.E2.m2aadec

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Defining formula

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

C1.S4.SS4.m1ahdec

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Legendre’s incomplete elliptic integral of the third kind

Defining formula

{\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}% \right)}}

C19.S2.E7.m2abdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3ahdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

C4.S23.SS2.p1.m7aadec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1idec

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Defining formula

{\displaystyle{\displaystyle p}}

C19.S2.XMD6.m1bdec

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Defining formula

{\displaystyle{\displaystyle k_{c}}}

C19.S2.XMD7.m1ddec

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Defining formula

{\displaystyle{\displaystyle x}}

C19.S2.XMD8.m1bdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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