DLMF:10.11.E7 (Q3110): 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.m2acdec

Revision as of 15:20, 2 January 2020

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DLMF:10.11.E7
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    Statements

    test
    H n ( 1 ) ⁡ ( z ⁢ e m ⁢ π ⁢ i ) = ( - 1 ) m ⁢ n - 1 ⁢ ( ( m - 1 ) ⁢ H n ( 1 ) ⁡ ( z ) + m ⁢ H n ( 2 ) ⁡ ( z ) ) , Hankel-H-1-Bessel-third-kind 𝑛 𝑧 superscript 𝑒 𝑚 𝜋 𝑖 superscript 1 𝑚 𝑛 1 𝑚 1 Hankel-H-1-Bessel-third-kind 𝑛 𝑧 𝑚 Hankel-H-2-Bessel-third-kind 𝑛 𝑧 {\displaystyle{\displaystyle{H^{(1)}_{n}}\left(ze^{m\pi i}\right)=(-1)^{mn-1}(% (m-1){H^{(1)}_{n}}\left(z\right)+m{H^{(2)}_{n}}\left(z\right)),}}
    0 references
    DLMF id
    DLMF:10.11.E7
    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.m2acdec
    0 references
     
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