DLMF:32.7.E4 (Q9282)

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DLMF:32.7.E4
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    Statements

    test
    w 2 ⁢ ( z ; 0 ) = 2 - 1 / 3 ⁢ ( W 2 ⁢ ( ζ ; 1 2 ⁢ ε ) - ε ⁢ d d ζ ⁡ W ⁢ ( ζ ; 1 2 ⁢ ε ) + 1 2 ⁢ ζ ) , superscript 𝑤 2 𝑧 0 superscript 2 1 3 superscript 𝑊 2 𝜁 1 2 𝜀 𝜀 derivative 𝜁 𝑊 𝜁 1 2 𝜀 1 2 𝜁 {\displaystyle{\displaystyle w^{2}(z;0)=2^{-1/3}\left(W^{2}(\zeta;\tfrac{1}{2}% \varepsilon)-\varepsilon\frac{\mathrm{d}}{\mathrm{d}\zeta}W(\zeta;\tfrac{1}{2}% \varepsilon)+\tfrac{1}{2}\zeta\right),}}
    0 references
    DLMF id
    DLMF:32.7.E4
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aadec
    0 references
    Q12523
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C32.S1.XMD4.m1cdec
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    Q12552
    test
    W ⁢ ( ζ , ε / 2 ) 𝑊 𝜁 𝜀 2 {\displaystyle{\displaystyle W(\zeta,\varepsilon/2)}}
    xml-id
    C32.S7.XMD3.m1adec
    0 references
     
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