DLMF:10.17.E15 (Q3184): Difference between revisions

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DLMF:10.17.E15
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    Statements

    Defining formula
    𝒱 z , i ⁒ ∞ ⁑ ( t - β„“ ) ≀ { | z | - β„“ , 0 ≀ ph ⁑ z ≀ Ο€ , Ο‡ ⁒ ( β„“ ) ⁒ | z | - β„“ , - 1 2 ⁒ Ο€ ≀ ph ⁑ z ≀ 0 Β orΒ  Ο€ ≀ ph ⁑ z ≀ 3 2 ⁒ Ο€ , 2 ⁒ Ο‡ ⁒ ( β„“ ) ⁒ | β„‘ ⁑ z | - β„“ , - Ο€ < ph ⁑ z ≀ - 1 2 ⁒ Ο€ Β orΒ  3 2 ⁒ Ο€ ≀ ph ⁑ z < 2 ⁒ Ο€ , variational-operator-on-interval 𝑧 𝑖 superscript 𝑑 β„“ cases superscript 𝑧 β„“ 0 phase 𝑧 πœ‹ πœ’ β„“ superscript 𝑧 β„“ - 1 2 ⁒ Ο€ ≀ ph ⁑ z ≀ 0 Β orΒ  Ο€ ≀ ph ⁑ z ≀ 3 2 ⁒ Ο€ , 2 πœ’ β„“ superscript 𝑧 β„“ - Ο€ < ph ⁑ z ≀ - 1 2 ⁒ Ο€ Β orΒ  3 2 ⁒ Ο€ ≀ ph ⁑ z < 2 ⁒ Ο€ , {\displaystyle{\displaystyle\mathcal{V}_{z,i\infty}\left(t^{-\ell}\right)\leq% \begin{cases}|z|^{-\ell},&0\leq\operatorname{ph}z\leq\pi,\\ \chi(\ell)|z|^{-\ell},&\parbox[t]{224.037pt}{$-\tfrac{1}{2}\pi\leq% \operatorname{ph}z\leq 0$ or $\pi\leq\operatorname{ph}z\leq\tfrac{3}{2}\pi$,}% \\ 2\chi(\ell)|\Im z|^{-\ell},&\parbox[t]{224.037pt}{$-\pi<\operatorname{ph}z\leq% -\tfrac{1}{2}\pi$ or $\tfrac{3}{2}\pi\leq\operatorname{ph}z<2\pi$,}\end{cases}}}
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    DLMF id
    DLMF:10.17.E15
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