DLMF:10.27.E11 (Q3501): Difference between revisions

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Property / constraint
 

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

-\tfrac{1}{2}\pi\leq\pm\phase@@{z}\leq\pi
Property / constraint: - 1 2 π ± ph z π 1 2 𝜋 plus-or-minus phase 𝑧 𝜋 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi\leq\pm\operatorname{ph}z\leq\pi}} / rank
 
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Revision as of 17:38, 30 December 2019

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DLMF:10.27.E11
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    Statements

    Y ν ( z ) = e ± ( ν + 1 ) π i / 2 I ν ( z e π i / 2 ) - ( 2 / π ) e ν π i / 2 K ν ( z e π i / 2 ) , Bessel-Y-Weber 𝜈 𝑧 superscript 𝑒 plus-or-minus 𝜈 1 𝜋 𝑖 2 modified-Bessel-first-kind 𝜈 𝑧 superscript 𝑒 minus-or-plus 𝜋 𝑖 2 2 𝜋 superscript 𝑒 minus-or-plus 𝜈 𝜋 𝑖 2 modified-Bessel-second-kind 𝜈 𝑧 superscript 𝑒 minus-or-plus 𝜋 𝑖 2 {\displaystyle{\displaystyle Y_{\nu}\left(z\right)=e^{\pm(\nu+1)\pi i/2}I_{\nu% }\left(ze^{\mp\pi i/2}\right)-(2/\pi)e^{\mp\nu\pi i/2}K_{\nu}\left(ze^{\mp\pi i% /2}\right),}}
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    - 1 2 π ± ph z π 1 2 𝜋 plus-or-minus phase 𝑧 𝜋 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi\leq\pm\operatorname{ph}z\leq\pi}}
    0 references