DLMF:19.24.E3 (Q6484): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of second kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of second kind / qualifier
 
test:

R G ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

\CarlsonsymellintRG@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: symmetric elliptic integral of second kind / qualifier
 
xml-id: C19.S16.E3.m2aadec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec

Latest revision as of 13:04, 2 January 2020

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DLMF:19.24.E3
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    Statements

    ( y 3 / 2 + z 3 / 2 2 ) 2 / 3 4 π R G ( 0 , y 2 , z 2 ) ( y 2 + z 2 2 ) 1 / 2 , superscript superscript 𝑦 3 2 superscript 𝑧 3 2 2 2 3 4 𝜋 Carlson-integral-RG 0 superscript 𝑦 2 superscript 𝑧 2 superscript superscript 𝑦 2 superscript 𝑧 2 2 1 2 {\displaystyle{\displaystyle\left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3}\leq% \frac{4}{\pi}R_{G}\left(0,y^{2},z^{2}\right)\leq\left(\frac{y^{2}+z^{2}}{2}% \right)^{1/2},}}
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    z > 0 𝑧 0 {\displaystyle{\displaystyle z>0}}
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    R G ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    C19.S16.E3.m2aadec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
    0 references