DLMF:10.27.E9 (Q3499): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1hdec

Revision as of 13:36, 2 January 2020

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DLMF:10.27.E9
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    Statements

    π i J ν ( z ) = e - ν π i / 2 K ν ( z e - π i / 2 ) - e ν π i / 2 K ν ( z e π i / 2 ) , 𝜋 𝑖 Bessel-J 𝜈 𝑧 superscript 𝑒 𝜈 𝜋 𝑖 2 modified-Bessel-second-kind 𝜈 𝑧 superscript 𝑒 𝜋 𝑖 2 superscript 𝑒 𝜈 𝜋 𝑖 2 modified-Bessel-second-kind 𝜈 𝑧 superscript 𝑒 𝜋 𝑖 2 {\displaystyle{\displaystyle\pi iJ_{\nu}\left(z\right)=e^{-\nu\pi i/2}K_{\nu}% \left(ze^{-\pi i/2}\right)-e^{\nu\pi i/2}K_{\nu}\left(ze^{\pi i/2}\right),}}
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    DLMF:10.27.E9
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    | ph z | 1 2 π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi}}
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    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2aadec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aedec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2acdec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2acdec
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    K ν ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.E3.m2aedec
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    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1acdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1hdec
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