DLMF:19.2.E22 (Q6118)

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DLMF:19.2.E22
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    Statements

    Defining formula
    R C ⁡ ( x , y ) = 2 π ⁢ ∫ 0 π / 2 R C ⁡ ( y , x ⁢ cos 2 ⁡ θ + y ⁢ sin 2 ⁡ θ ) ⁢ d θ . Carlson-integral-RC 𝑥 𝑦 2 𝜋 superscript subscript 0 𝜋 2 Carlson-integral-RC 𝑦 𝑥 2 𝜃 𝑦 2 𝜃 𝜃 {\displaystyle{\displaystyle R_{C}\left(x,y\right)=\frac{2}{\pi}\int_{0}^{\pi/% 2}R_{C}\left(y,x{\cos^{2}}\theta+y{\sin^{2}}\theta\right)\mathrm{d}\theta.}}
    0 references
    DLMF id
    DLMF:19.2.E22
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    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    Defining formula
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2aedec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
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