DLMF:19.25.E5 (Q6509)

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DLMF:19.25.E5
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    Statements

    Defining formula
    F ⁡ ( ϕ , k ) = R F ⁡ ( c - 1 , c - k 2 , c ) , elliptic-integral-first-kind-F italic-ϕ 𝑘 Carlson-integral-RF 𝑐 1 𝑐 superscript 𝑘 2 𝑐 {\displaystyle{\displaystyle F\left(\phi,k\right)=R_{F}\left(c-1,c-k^{2},c% \right),}}
    0 references
    DLMF id
    DLMF:19.25.E5
    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.m2aadec
    0 references
    Legendre’s incomplete elliptic integral of the first kind
    Defining formula
    F ⁡ ( ϕ , k ) elliptic-integral-first-kind-F italic-ϕ 𝑘 {\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}
    xml-id
    C19.S2.E4.m2adec
    0 references
     
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