DLMF:19.24.E2 (Q6483): Difference between revisions

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Property / constraint
 

0 y z 0 𝑦 𝑧 {\displaystyle{\displaystyle 0\leq y\leq z}}

0\leq y\leq z
Property / constraint: 0 y z 0 𝑦 𝑧 {\displaystyle{\displaystyle 0\leq y\leq z}} / rank
 
Normal rank
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
 
Defining formula:

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.m2adec
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
 
Defining formula:

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.m2aadec

Latest revision as of 14:03, 2 January 2020

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DLMF:19.24.E2
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    Statements

    1 2 z - 1 / 2 R G ( 0 , y , z ) 1 4 π , 1 2 superscript 𝑧 1 2 Carlson-integral-RG 0 𝑦 𝑧 1 4 𝜋 {\displaystyle{\displaystyle\tfrac{1}{2}\leq z^{-1/2}R_{G}\left(0,y,z\right)% \leq\tfrac{1}{4}\pi,}}
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    DLMF:19.24.E2
    0 references
    0 y z 0 𝑦 𝑧 {\displaystyle{\displaystyle 0\leq y\leq z}}
    0 references
    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.m2adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references