DLMF:19.29.E19 (Q6647): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11908 / rank
 
Normal rank
Property / Symbols used: Q11908 / qualifier
 
test:

U 𝑈 {\displaystyle{\displaystyle U}}

U
Property / Symbols used: Q11908 / qualifier
 
xml-id: C19.S29.XMD16.m1dec
Property / Symbols used
 
Property / Symbols used: Q11909 / rank
 
Normal rank
Property / Symbols used: Q11909 / qualifier
 
test:

Q ⁢ ( t 2 ) 𝑄 superscript 𝑡 2 {\displaystyle{\displaystyle Q(t^{2})}}

Q(t^{2})
Property / Symbols used: Q11909 / qualifier
 
xml-id: C19.S29.XMD24.m1dec

Latest revision as of 13:20, 2 January 2020

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DLMF:19.29.E19
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    Statements

    test
    ∫ y x d t Q 1 ⁢ ( t ) ⁢ Q 2 ⁢ ( t ) = R F ⁡ ( U 2 + a 1 ⁢ b 2 , U 2 + a 2 ⁢ b 1 , U 2 ) , superscript subscript 𝑦 𝑥 𝑡 subscript 𝑄 1 𝑡 subscript 𝑄 2 𝑡 Carlson-integral-RF superscript 𝑈 2 subscript 𝑎 1 subscript 𝑏 2 superscript 𝑈 2 subscript 𝑎 2 subscript 𝑏 1 superscript 𝑈 2 {\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{Q_{1}(t)Q_{2}% (t)}}=R_{F}\left(U^{2}+a_{1}b_{2},U^{2}+a_{2}b_{1},U^{2}\right),}}
    0 references
    DLMF id
    DLMF:19.29.E19
    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.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    Q11908
    test
    U 𝑈 {\displaystyle{\displaystyle U}}
    xml-id
    C19.S29.XMD16.m1dec
    0 references
    Q11909
    test
    Q ⁢ ( t 2 ) 𝑄 superscript 𝑡 2 {\displaystyle{\displaystyle Q(t^{2})}}
    xml-id
    C19.S29.XMD24.m1dec
    0 references
     
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