DLMF:19.30.E12 (Q6687)

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DLMF:19.30.E12
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    Statements

    Defining formula
    s = a ⁢ F ⁡ ( ϕ , 1 / 2 ) , 𝑠 𝑎 elliptic-integral-first-kind-F italic-ϕ 1 2 {\displaystyle{\displaystyle s=aF\left(\phi,1/\sqrt{2}\right),}}
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    DLMF id
    DLMF:19.30.E12
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    constraint
    ϕ = arcsin ⁡ 2 / ( q + 1 ) = arccos ⁡ ( tan ⁡ θ ) italic-ϕ 2 𝑞 1 𝜃 {\displaystyle{\displaystyle\phi=\operatorname{arcsin}\sqrt{2/(q+1)}=% \operatorname{arccos}\left(\tan\theta\right)}}
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    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.m2aadec
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    Q11208
    Defining formula
    arccos ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m6adec
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    Q11242
    Defining formula
    arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m5adec
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