DLMF:10.47.E5 (Q3673): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Bessel function of the third kind (or Hankel function) / rank
 
Normal rank
Property / Symbols used: Bessel function of the third kind (or Hankel function) / qualifier
 
test:

H ν ( 1 ) ⁡ ( z ) Hankel-H-1-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}

\HankelH{1}{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the third kind (or Hankel function) / qualifier
 
xml-id: C10.S2.E5.m2adec

Revision as of 13:08, 2 January 2020

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DLMF:10.47.E5
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    Statements

    test
    𝗁 n ( 1 ) ⁡ ( z ) = 1 2 ⁢ π / z ⁢ H n + 1 2 ( 1 ) ⁡ ( z ) = ( - 1 ) n + 1 ⁢ i ⁢ 1 2 ⁢ π / z ⁢ H - n - 1 2 ( 1 ) ⁡ ( z ) , spherical-Hankel-H-1-Bessel-third-kind 𝑛 𝑧 1 2 𝜋 𝑧 Hankel-H-1-Bessel-third-kind 𝑛 1 2 𝑧 superscript 1 𝑛 1 imaginary-unit 1 2 𝜋 𝑧 Hankel-H-1-Bessel-third-kind 𝑛 1 2 𝑧 {\displaystyle{\displaystyle{\mathsf{h}^{(1)}_{n}}\left(z\right)=\sqrt{\tfrac{% 1}{2}\pi/z}{H^{(1)}_{n+\frac{1}{2}}}\left(z\right)=(-1)^{n+1}\mathrm{i}\sqrt{% \tfrac{1}{2}\pi/z}{H^{(1)}_{-n-\frac{1}{2}}}\left(z\right),}}
    0 references
    DLMF id
    DLMF:10.47.E5
    0 references
    Symbols used
    Bessel function of the third kind (or Hankel function)
    test
    H ν ( 1 ) ⁡ ( z ) Hankel-H-1-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E5.m2adec
    0 references
     
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