DLMF:10.11.E4 (Q3106): 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 15:20, 2 January 2020

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DLMF:10.11.E4
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    Defining formula
    sin ⁡ ( ν ⁢ π ) ⁢ H ν ( 2 ) ⁡ ( z ⁢ e m ⁢ π ⁢ i ) = e ν ⁢ π ⁢ i ⁢ sin ⁡ ( m ⁢ ν ⁢ π ) ⁢ H ν ( 1 ) ⁡ ( z ) + sin ⁡ ( ( m + 1 ) ⁢ ν ⁢ π ) ⁢ H ν ( 2 ) ⁡ ( z ) . 𝜈 𝜋 Hankel-H-2-Bessel-third-kind 𝜈 𝑧 superscript 𝑒 𝑚 𝜋 𝑖 superscript 𝑒 𝜈 𝜋 𝑖 𝑚 𝜈 𝜋 Hankel-H-1-Bessel-third-kind 𝜈 𝑧 𝑚 1 𝜈 𝜋 Hankel-H-2-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle\sin\left(\nu\pi\right){H^{(2)}_{\nu}}\left(ze^{m% \pi i}\right)=e^{\nu\pi i}\sin\left(m\nu\pi\right){H^{(1)}_{\nu}}\left(z\right% )+\sin\left((m+1)\nu\pi\right){H^{(2)}_{\nu}}\left(z\right).}}
    0 references
    DLMF id
    DLMF:10.11.E4
    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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