DLMF:19.24.E4 (Q6485): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of third kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
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)}}

\CarlsonsymellintRJ@{\NVar{x}}{\NVar{y}}{\NVar{z}}{\NVar{p}}
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
xml-id: C19.S16.E2.m2adec

Revision as of 14:04, 2 January 2020

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DLMF:19.24.E4
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    Statements

    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}.}}
    0 references
    DLMF:19.24.E4
    0 references
    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)}}
    C19.S16.E2.m2adec
    0 references