DLMF:19.24.E9 (Q6492): Difference between revisions

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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
 
test:

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.m2acdec
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.m2addec
Property / Symbols used
 
Property / Symbols used: Q11824 / rank
 
Normal rank
Property / Symbols used: Q11824 / qualifier
 
test:

a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}

a_{n}
Property / Symbols used: Q11824 / qualifier
 
xml-id: C19.S8.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11825 / rank
 
Normal rank
Property / Symbols used: Q11825 / qualifier
 
test:

g n subscript 𝑔 𝑛 {\displaystyle{\displaystyle g_{n}}}

g_{n}
Property / Symbols used: Q11825 / qualifier
 
xml-id: C19.S8.XMD2.m1bdec

Latest revision as of 13:04, 2 January 2020

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DLMF:19.24.E9
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    Statements

    test
    1 2 ⁢ g 1 2 ≤ R G ⁡ ( a 0 2 , g 0 2 , 0 ) R F ⁡ ( a 0 2 , g 0 2 , 0 ) ≤ 1 2 ⁢ a 1 2 , 1 2 superscript subscript 𝑔 1 2 Carlson-integral-RG superscript subscript 𝑎 0 2 superscript subscript 𝑔 0 2 0 Carlson-integral-RF superscript subscript 𝑎 0 2 superscript subscript 𝑔 0 2 0 1 2 superscript subscript 𝑎 1 2 {\displaystyle{\displaystyle\frac{1}{2}\,g_{1}^{2}\leq\frac{R_{G}\left(a_{0}^{% 2},g_{0}^{2},0\right)}{R_{F}\left(a_{0}^{2},g_{0}^{2},0\right)}\leq\frac{1}{2}% \,a_{1}^{2},}}
    0 references
    DLMF id
    DLMF:19.24.E9
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    test
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2acdec
    0 references
    symmetric elliptic integral of second kind
    test
    R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E3.m2addec
    0 references
    Q11824
    test
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C19.S8.XMD1.m1bdec
    0 references
    Q11825
    test
    g n subscript 𝑔 𝑛 {\displaystyle{\displaystyle g_{n}}}
    xml-id
    C19.S8.XMD2.m1bdec
    0 references
     
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