DLMF:19.25.E17 (Q6521)

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DLMF:19.25.E17
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    Statements

    Defining formula
    F ⁑ ( Ο• , k ) = R F ⁑ ( x , y , z ) , elliptic-integral-first-kind-F italic-Ο• π‘˜ Carlson-integral-RF π‘₯ 𝑦 𝑧 {\displaystyle{\displaystyle F\left(\phi,k\right)=R_{F}\left(x,y,z\right),}}
    0 references
    DLMF id
    DLMF:19.25.E17
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁑ ( x , y , z ) Carlson-integral-RF π‘₯ 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2aedec
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    Legendre’s incomplete elliptic integral of the first kind
    Defining formula
    F ⁑ ( Ο• , k ) elliptic-integral-first-kind-F italic-Ο• π‘˜ {\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}
    xml-id
    C19.S2.E4.m2acdec
    0 references
    Q11807
    Defining formula
    Ο• italic-Ο• {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1ldec
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    Q11808
    Defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1pdec
    0 references
     
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