DLMF:19.23.E5 (Q6476)

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Language	Label	Description	Also known as
English	DLMF:19.23.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle R_{F}\left(x,y,z\right)=\frac{2}{\pi}\int_{0}^{% \pi/2}R_{C}\left(x,y{\cos^{2}}\theta+z{\sin^{2}}\theta\right)\mathrm{d}\theta,}}

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DLMF:19.23.E5

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{\displaystyle{\displaystyle\Re y>0}}

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{\displaystyle{\displaystyle\Re z>0}}

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Carlson’s combination of inverse circular and inverse hyperbolic functions

Defining formula

{\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}

C19.S2.E17.m2aadec

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symmetric elliptic integral of first kind

Defining formula

{\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

C19.S16.E1.m2abdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2addec

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cosine function

Defining formula

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

C4.S14.E2.m2addec

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Defining formula

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

C1.S4.SS4.m1addec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3addec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1adec

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Defining formula

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

C4.S14.E1.m2acdec

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Sitelinks

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