DLMF:19.28.E9 (Q6617)

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DLMF:19.28.E9
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    Statements

    Defining formula
    ∫ 0 π / 2 R F ⁡ ( sin 2 ⁡ θ ⁢ cos 2 ⁡ ( x + y ) , sin 2 ⁡ θ ⁢ cos 2 ⁡ ( x - y ) , 1 ) ⁢ d θ = R F ⁡ ( 0 , cos 2 ⁡ x , 1 ) ⁢ R F ⁡ ( 0 , cos 2 ⁡ y , 1 ) , superscript subscript 0 𝜋 2 Carlson-integral-RF 2 𝜃 2 𝑥 𝑦 2 𝜃 2 𝑥 𝑦 1 𝜃 Carlson-integral-RF 0 2 𝑥 1 Carlson-integral-RF 0 2 𝑦 1 {\displaystyle{\displaystyle\int_{0}^{\pi/2}R_{F}\left({\sin^{2}}\theta{\cos^{% 2}}\left(x+y\right),{\sin^{2}}\theta{\cos^{2}}\left(x-y\right),1\right)\mathrm% {d}\theta=R_{F}\left(0,{\cos^{2}}x,1\right)R_{F}\left(0,{\cos^{2}}y,1\right),}}
    0 references
    DLMF id
    DLMF:19.28.E9
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
     
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