DLMF:19.9.E13 (Q6256)

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DLMF:19.9.E13
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    Statements

    Defining formula
    Π ⁡ ( ϕ , α 2 , 0 ) ≤ Π ⁡ ( ϕ , α 2 , k ) ≤ min ⁡ ( Π ⁡ ( ϕ , α 2 , 0 ) / Δ , Π ⁡ ( ϕ , α 2 , 1 ) ) . elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 0 elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 𝑘 elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 0 Δ elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 1 {\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},0\right)\leq\Pi\left(\phi% ,\alpha^{2},k\right)\leq\min(\Pi\left(\phi,\alpha^{2},0\right)/\Delta,\Pi\left% (\phi,\alpha^{2},1\right)).}}
    0 references
    DLMF id
    DLMF:19.9.E13
    0 references
    Symbols used
    Legendre’s incomplete elliptic integral of the third kind
    Defining formula
    Π ⁡ ( ϕ , α 2 , k ) elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 𝑘 {\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}% \right)}}
    xml-id
    C19.S2.E7.m2adec
    0 references
    Q11807
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1bdec
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    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1kdec
    0 references
    Q11809
    Defining formula
    α 2 superscript 𝛼 2 {\displaystyle{\displaystyle\alpha^{2}}}
    xml-id
    C19.S1.XMD7.m1adec
    0 references
     
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