DLMF:10.5.E5 (Q3028): 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
 
Defining formula:

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.m2aadec

Revision as of 15:07, 2 January 2020

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DLMF:10.5.E5
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    Statements

    Defining formula
    𝒲 ⁡ { H ν ( 1 ) ⁡ ( z ) , H ν ( 2 ) ⁡ ( z ) } = H ν + 1 ( 1 ) ⁡ ( z ) ⁢ H ν ( 2 ) ⁡ ( z ) - H ν ( 1 ) ⁡ ( z ) ⁢ H ν + 1 ( 2 ) ⁡ ( z ) = - 4 ⁢ i / ( π ⁢ z ) . Wronskian Hankel-H-1-Bessel-third-kind 𝜈 𝑧 Hankel-H-2-Bessel-third-kind 𝜈 𝑧 Hankel-H-1-Bessel-third-kind 𝜈 1 𝑧 Hankel-H-2-Bessel-third-kind 𝜈 𝑧 Hankel-H-1-Bessel-third-kind 𝜈 𝑧 Hankel-H-2-Bessel-third-kind 𝜈 1 𝑧 4 𝑖 𝜋 𝑧 {\displaystyle{\displaystyle\mathscr{W}\left\{{H^{(1)}_{\nu}}\left(z\right),{H% ^{(2)}_{\nu}}\left(z\right)\right\}={H^{(1)}_{\nu+1}}\left(z\right){H^{(2)}_{% \nu}}\left(z\right)-{H^{(1)}_{\nu}}\left(z\right){H^{(2)}_{\nu+1}}\left(z% \right)=-4i/(\pi z).}}
    0 references
    DLMF id
    DLMF:10.5.E5
    0 references
    Symbols used
    Bessel function of the third kind (or Hankel function)
    Defining formula
    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.m2aadec
    0 references
     
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