DLMF:19.29.E32 (Q6671): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11908 / rank
 
Normal rank
Property / Symbols used: Q11908 / qualifier
 
Defining formula:

U 𝑈 {\displaystyle{\displaystyle U}}

U
Property / Symbols used: Q11908 / qualifier
 
xml-id: C19.S29.XMD16.m1jdec

Latest revision as of 14:22, 2 January 2020

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DLMF:19.29.E32
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    Statements

    y x d t t 4 + a 4 = 2 R F ( U , U + 2 a 2 , U - 2 a 2 ) , superscript subscript 𝑦 𝑥 𝑡 superscript 𝑡 4 superscript 𝑎 4 2 Carlson-integral-RF 𝑈 𝑈 2 superscript 𝑎 2 𝑈 2 superscript 𝑎 2 {\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{t^{4}+a^{4}}}% =2R_{F}\left(U,U+2a^{2},U-2a^{2}\right),}}
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    DLMF:19.29.E32
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    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.m2afdec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aldec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aldec
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    U 𝑈 {\displaystyle{\displaystyle U}}
    C19.S29.XMD16.m1jdec
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