DLMF:10.17.E10 (Q3179): Difference between revisions

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

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

Revision as of 17:17, 30 December 2019

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DLMF:10.17.E10
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    Y ν ( z ) ( 2 π z ) 1 2 ( cos ω k = 0 ( - 1 ) k b 2 k ( ν ) z 2 k - sin ω k = 0 ( - 1 ) k b 2 k + 1 ( ν ) z 2 k + 1 ) , asymptotic-expansion diffop Bessel-Y-Weber 𝜈 1 𝑧 superscript 2 𝜋 𝑧 1 2 𝜔 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑏 2 𝑘 𝜈 superscript 𝑧 2 𝑘 𝜔 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑏 2 𝑘 1 𝜈 superscript 𝑧 2 𝑘 1 {\displaystyle{\displaystyle Y_{\nu}'\left(z\right)\sim\left(\frac{2}{\pi z}% \right)^{\frac{1}{2}}\left(\cos\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{b_{2k}(% \nu)}{z^{2k}}-\sin\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{b_{2k+1}(\nu)}{z^{2k+% 1}}\right),}}
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    DLMF:10.17.E10
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    | ph z | π - δ phase 𝑧 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}
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