DLMF:10.17.E12 (Q3181): Difference between revisions

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Property / constraint
 

- 2 π + δ ph z π - δ 2 𝜋 𝛿 phase 𝑧 𝜋 𝛿 {\displaystyle{\displaystyle-2\pi+\delta\leq\operatorname{ph}z\leq\pi-\delta}}

-2\pi+\delta\leq\phase@@{z}\leq\pi-\delta
Property / constraint: - 2 π + δ ph z π - δ 2 𝜋 𝛿 phase 𝑧 𝜋 𝛿 {\displaystyle{\displaystyle-2\pi+\delta\leq\operatorname{ph}z\leq\pi-\delta}} / rank
 
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Revision as of 16:17, 30 December 2019

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DLMF:10.17.E12
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    Statements

    H ν ( 2 ) ( z ) - i ( 2 π z ) 1 2 e - i ω k = 0 ( - i ) k b k ( ν ) z k , asymptotic-expansion diffop Hankel-H-2-Bessel-third-kind 𝜈 1 𝑧 𝑖 superscript 2 𝜋 𝑧 1 2 superscript 𝑒 𝑖 𝜔 superscript subscript 𝑘 0 superscript 𝑖 𝑘 subscript 𝑏 𝑘 𝜈 superscript 𝑧 𝑘 {\displaystyle{\displaystyle{H^{(2)}_{\nu}}'\left(z\right)\sim-i\left(\frac{2}% {\pi z}\right)^{\frac{1}{2}}e^{-i\omega}\sum_{k=0}^{\infty}(-i)^{k}\frac{b_{k}% (\nu)}{z^{k}},}}
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    - 2 π + δ ph z π - δ 2 𝜋 𝛿 phase 𝑧 𝜋 𝛿 {\displaystyle{\displaystyle-2\pi+\delta\leq\operatorname{ph}z\leq\pi-\delta}}
    0 references