DLMF:10.30.E5 (Q3517): Difference between revisions

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Property / constraint
 

1 2 π + δ ± ph z 3 2 π - δ 1 2 𝜋 𝛿 plus-or-minus phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle\tfrac{1}{2}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{3}{2}\pi-\delta}}

\tfrac{1}{2}\pi+\delta\leq\pm\phase@@{z}\leq\tfrac{3}{2}\pi-\delta
Property / constraint: 1 2 π + δ ± ph z 3 2 π - δ 1 2 𝜋 𝛿 plus-or-minus phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle\tfrac{1}{2}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{3}{2}\pi-\delta}} / rank
 
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Revision as of 16:38, 30 December 2019

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DLMF:10.30.E5
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    Statements

    I ν ( z ) e ± ( ν + 1 2 ) π i e - z / 2 π z , asymptotically-equals modified-Bessel-first-kind 𝜈 𝑧 superscript 𝑒 plus-or-minus 𝜈 1 2 𝜋 𝑖 superscript 𝑒 𝑧 2 𝜋 𝑧 {\displaystyle{\displaystyle I_{\nu}\left(z\right)\sim e^{\pm(\nu+\frac{1}{2})% \pi i}e^{-z}/\sqrt{2\pi z},}}
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    1 2 π + δ ± ph z 3 2 π - δ 1 2 𝜋 𝛿 plus-or-minus phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle\tfrac{1}{2}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{3}{2}\pi-\delta}}
    0 references