DLMF:19.11.E7 (Q6281)

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DLMF:19.11.E7
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    Statements

    Defining formula
    F ⁡ ( ϕ , k ) = K ⁡ ( k ) - F ⁡ ( θ , k ) , elliptic-integral-first-kind-F italic-ϕ 𝑘 complete-elliptic-integral-first-kind-K 𝑘 elliptic-integral-first-kind-F 𝜃 𝑘 {\displaystyle{\displaystyle F\left(\phi,k\right)=K\left(k\right)-F\left(% \theta,k\right),}}
    0 references
    DLMF id
    DLMF:19.11.E7
    0 references
    Symbols used
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1adec
    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.m2aadec
    0 references
    Q11807
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1fdec
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