DLMF:10.17.E11 (Q3180): Difference between revisions

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Property / constraint
 

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

-\pi+\delta\leq\phase@@{z}\leq 2\pi-\delta
Property / constraint: - π + δ ph z 2 π - δ 𝜋 𝛿 phase 𝑧 2 𝜋 𝛿 {\displaystyle{\displaystyle-\pi+\delta\leq\operatorname{ph}z\leq 2\pi-\delta}} / rank
 
Normal rank

Revision as of 16:17, 30 December 2019

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DLMF:10.17.E11
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    Statements

    H ν ( 1 ) ( z ) i ( 2 π z ) 1 2 e i ω k = 0 i k b k ( ν ) z k , asymptotic-expansion diffop Hankel-H-1-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^{(1)}_{\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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    - π + δ ph z 2 π - δ 𝜋 𝛿 phase 𝑧 2 𝜋 𝛿 {\displaystyle{\displaystyle-\pi+\delta\leq\operatorname{ph}z\leq 2\pi-\delta}}
    0 references