DLMF:10.47.E6 (Q3674)

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DLMF:10.47.E6
No description defined

    Statements

    Defining formula
    𝗁 n ( 2 ) ⁡ ( z ) = 1 2 ⁢ π / z ⁢ H n + 1 2 ( 2 ) ⁡ ( z ) = ( - 1 ) n ⁢ i ⁢ 1 2 ⁢ π / z ⁢ H - n - 1 2 ( 2 ) ⁡ ( z ) . spherical-Hankel-H-2-Bessel-third-kind 𝑛 𝑧 1 2 𝜋 𝑧 Hankel-H-2-Bessel-third-kind 𝑛 1 2 𝑧 superscript 1 𝑛 imaginary-unit 1 2 𝜋 𝑧 Hankel-H-2-Bessel-third-kind 𝑛 1 2 𝑧 {\displaystyle{\displaystyle{\mathsf{h}^{(2)}_{n}}\left(z\right)=\sqrt{\tfrac{% 1}{2}\pi/z}{H^{(2)}_{n+\frac{1}{2}}}\left(z\right)=(-1)^{n}\mathrm{i}\sqrt{% \tfrac{1}{2}\pi/z}{H^{(2)}_{-n-\frac{1}{2}}}\left(z\right).}}
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    DLMF id
    DLMF:10.47.E6
    0 references
    Symbols used
    Bessel function of the third kind (or Hankel function)
    Defining formula
    H ν ( 2 ) ⁡ ( z ) Hankel-H-2-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E6.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1edec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1edec
    0 references
     
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