DLMF:19.29.E28 (Q6665): Difference between revisions

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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.m1fdec

Latest revision as of 14:21, 2 January 2020

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DLMF:19.29.E28
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    Statements

    Defining formula
    ∫ y x d t t 3 - a 3 = 4 ⁢ R F ⁡ ( U , U - 3 ⁢ a + 2 ⁢ 3 ⁢ a , U - 3 ⁢ a - 2 ⁢ 3 ⁢ a ) , superscript subscript 𝑦 𝑥 𝑡 superscript 𝑡 3 superscript 𝑎 3 4 Carlson-integral-RF 𝑈 𝑈 3 𝑎 2 3 𝑎 𝑈 3 𝑎 2 3 𝑎 {\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{t^{3}-a^{3}}}% =4R_{F}\left(U,U-3a+2\sqrt{3}a,U-3a-2\sqrt{3}a\right),}}
    0 references
    DLMF id
    DLMF:19.29.E28
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    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)}}
    xml-id
    C19.S16.E1.m2addec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
    0 references
    Q11908
    Defining formula
    U 𝑈 {\displaystyle{\displaystyle U}}
    xml-id
    C19.S29.XMD16.m1fdec
    0 references
     
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