DLMF:19.24.E4 (Q6485)

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DLMF:19.24.E4
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    Statements

    Defining formula
    2 p ⁢ ( 2 ⁢ y ⁢ z + y ⁢ p + z ⁢ p ) - 1 / 2 ≤ 4 3 ⁢ π ⁢ R J ⁡ ( 0 , y , z , p ) ≤ ( y ⁢ z ⁢ p 2 ) - 3 / 8 . 2 𝑝 superscript 2 𝑦 𝑧 𝑦 𝑝 𝑧 𝑝 1 2 4 3 𝜋 Carlson-integral-RJ 0 𝑦 𝑧 𝑝 superscript 𝑦 𝑧 superscript 𝑝 2 3 8 {\displaystyle{\displaystyle\frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2}\leq\frac{4}{3% \pi}R_{J}\left(0,y,z,p\right)\leq(yzp^{2})^{-3/8}.}}
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    DLMF id
    DLMF:19.24.E4
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    Symbols used
    symmetric elliptic integral of third kind
    Defining formula
    R J ⁡ ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}
    xml-id
    C19.S16.E2.m2adec
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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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