DLMF:19.11.E12 (Q6287)

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DLMF:19.11.E12
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    Statements

    Defining formula
    F ⁡ ( ψ , k ) = 2 ⁢ F ⁡ ( θ , k ) , elliptic-integral-first-kind-F 𝜓 𝑘 2 elliptic-integral-first-kind-F 𝜃 𝑘 {\displaystyle{\displaystyle F\left(\psi,k\right)=2F\left(\theta,k\right),}}
    0 references
    DLMF id
    DLMF:19.11.E12
    0 references
    Symbols used
    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.m2abdec
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    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1jdec
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    Q11842
    Defining formula
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C19.S11.XMD1.m1kdec
    0 references
    angle (locally)
    Defining formula
    ψ 𝜓 {\displaystyle{\displaystyle\psi}}
    xml-id
    C19.S11.XMD8.m1dec
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