DLMF:19.9.E17 (Q6260)

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DLMF:19.9.E17
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    Statements

    Defining formula
    L ≤ F ⁡ ( ϕ , k ) ≤ U ⁢ L ≤ 1 2 ⁢ ( U + L ) ≤ U , 𝐿 elliptic-integral-first-kind-F italic-ϕ 𝑘 𝑈 𝐿 1 2 𝑈 𝐿 𝑈 {\displaystyle{\displaystyle L\leq F\left(\phi,k\right)\leq\sqrt{UL}\leq\tfrac% {1}{2}(U+L)\leq U,}}
    0 references
    DLMF id
    DLMF:19.9.E17
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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.m2addec
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    Q11807
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1fdec
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    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1odec
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    Q11840
    Defining formula
    L 𝐿 {\displaystyle{\displaystyle L}}
    xml-id
    C19.S9.XMD3.m1dec
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    Q11841
    Defining formula
    U 𝑈 {\displaystyle{\displaystyle U}}
    xml-id
    C19.S9.XMD4.m1dec
    0 references
     
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