DLMF:19.24.E1 (Q6482): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of first kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of first kind / qualifier
 
Defining formula:

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

\CarlsonsymellintRF@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: symmetric elliptic integral of first kind / qualifier
 
xml-id: C19.S16.E1.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.m2adec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec

Latest revision as of 14:03, 2 January 2020

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DLMF:19.24.E1
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    Statements

    ln 4 z R F ( 0 , y , z ) + ln y / z 1 2 π , 4 𝑧 Carlson-integral-RF 0 𝑦 𝑧 𝑦 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\ln 4\leq\sqrt{z}R_{F}\left(0,y,z\right)+\ln\sqrt{% y/z}\leq\tfrac{1}{2}\pi,}}
    0 references
    DLMF:19.24.E1
    0 references
    0 < y z 0 𝑦 𝑧 {\displaystyle{\displaystyle 0<y\leq z}}
    0 references
    R F ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    C19.S16.E1.m2adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2adec
    0 references