DLMF:10.40.E12 (Q3590)

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DLMF:10.40.E12
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    Statements

    Defining formula
    𝒱 z , ∞ ⁡ ( t - ℓ ) ≤ { | z | - ℓ , | ph ⁡ z | ≤ 1 2 ⁢ π , χ ⁢ ( ℓ ) ⁢ | z | - ℓ , 1 2 ⁢ π ≤ | ph ⁡ z | ≤ π , 2 ⁢ χ ⁢ ( ℓ ) ⁢ | ℜ ⁡ z | - ℓ , π ≤ | ph ⁡ z | < 3 2 ⁢ π , variational-operator-on-interval 𝑧 superscript 𝑡 ℓ cases superscript 𝑧 ℓ phase 𝑧 1 2 𝜋 𝜒 ℓ superscript 𝑧 ℓ 1 2 𝜋 phase 𝑧 𝜋 2 𝜒 ℓ superscript 𝑧 ℓ 𝜋 phase 𝑧 3 2 𝜋 {\displaystyle{\displaystyle\mathcal{V}_{z,\infty}\left(t^{-\ell}\right)\leq% \begin{cases}|z|^{-\ell},&|\operatorname{ph}z|\leq\tfrac{1}{2}\pi,\\ \chi(\ell)|z|^{-\ell},&\tfrac{1}{2}\pi\leq|\operatorname{ph}z|\leq\pi,\\ 2\chi(\ell)|\Re z|^{-\ell},&\pi\leq|\operatorname{ph}z|<\tfrac{3}{2}\pi,\end{% cases}}}
    0 references
    DLMF id
    DLMF:10.40.E12
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aedec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    total variation
    Defining formula
    𝒱 a , b ⁡ ( f ) variational-operator-on-interval 𝑎 𝑏 𝑓 {\displaystyle{\displaystyle\mathcal{V}_{\NVar{a,b}}\left(\NVar{f}\right)}}
    xml-id
    C1.S4.E33.m2aadec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1jdec
    0 references
     
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