DLMF:19.25.E24 (Q6530)

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DLMF:19.25.E24
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    Statements

    Defining formula
    ( z - x ) 1 / 2 ⁒ R F ⁑ ( x , y , z ) = F ⁑ ( Ο• , k ) , superscript 𝑧 π‘₯ 1 2 Carlson-integral-RF π‘₯ 𝑦 𝑧 elliptic-integral-first-kind-F italic-Ο• π‘˜ {\displaystyle{\displaystyle(z-x)^{1/2}R_{F}\left(x,y,z\right)=F\left(\phi,k% \right),}}
    0 references
    DLMF id
    DLMF:19.25.E24
    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.m2ahdec
    0 references
    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.m2addec
    0 references
    Q11807
    Defining formula
    Ο• italic-Ο• {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1ndec
    0 references
    Q11808
    Defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1wdec
    0 references
     
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