DLMF:19.9.E14 (Q6257)

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DLMF:19.9.E14
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    Statements

    Defining formula
    3 1 + Δ + cos ⁡ ϕ < F ⁡ ( ϕ , k ) sin ⁡ ϕ < 1 ( Δ ⁢ cos ⁡ ϕ ) 1 / 3 , 3 1 Δ italic-ϕ elliptic-integral-first-kind-F italic-ϕ 𝑘 italic-ϕ 1 superscript Δ italic-ϕ 1 3 {\displaystyle{\displaystyle\frac{3}{1+\Delta+\cos\phi}<\frac{F\left(\phi,k% \right)}{\sin\phi}<\frac{1}{(\Delta\cos\phi)^{1/3}},}}
    0 references
    DLMF id
    DLMF:19.9.E14
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    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
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q11807
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1cdec
    0 references
     
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