DLMF:19.29.E30 (Q6669)

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DLMF:19.29.E30
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    Statements

    Defining formula
    ∫ y x d t Q ⁢ ( t 2 ) = 2 ⁢ R F ⁡ ( U , U - g + 2 ⁢ f ⁢ h , U - g - 2 ⁢ f ⁢ h ) , superscript subscript 𝑦 𝑥 𝑡 𝑄 superscript 𝑡 2 2 Carlson-integral-RF 𝑈 𝑈 𝑔 2 𝑓 ℎ 𝑈 𝑔 2 𝑓 ℎ {\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{Q(t^{2})}}=2R% _{F}\left(U,U-g+2\sqrt{fh},U-g-2\sqrt{fh}\right),}}
    0 references
    DLMF id
    DLMF:19.29.E30
    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.m2aedec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
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    Q11908
    Defining formula
    U 𝑈 {\displaystyle{\displaystyle U}}
    xml-id
    C19.S29.XMD16.m1hdec
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    Q11909
    Defining formula
    Q ⁢ ( t 2 ) 𝑄 superscript 𝑡 2 {\displaystyle{\displaystyle Q(t^{2})}}
    xml-id
    C19.S29.XMD24.m1fdec
    0 references
    Q11912
    Defining formula
    f 𝑓 {\displaystyle{\displaystyle f}}
    xml-id
    C19.S29.XMD25.m1bdec
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    Q11913
    Defining formula
    g 𝑔 {\displaystyle{\displaystyle g}}
    xml-id
    C19.S29.XMD26.m1cdec
    0 references
    Q11914
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C19.S29.XMD27.m1cdec
    0 references
     
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