DLMF:9.6.E20 (Q2800)

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DLMF:9.6.E20
No description defined

    Statements

    Defining formula
    H 2 / 3 ( 2 ) ⁡ ( ζ ) = e 2 ⁢ π ⁢ i / 3 ⁢ H - 2 / 3 ( 2 ) ⁡ ( ζ ) = e - π ⁢ i / 6 ⁢ ( 3 / z ) ⁢ ( Ai ′ ⁡ ( - z ) + i ⁢ Bi ′ ⁡ ( - z ) ) . Hankel-H-2-Bessel-third-kind 2 3 𝜁 superscript 𝑒 2 𝜋 𝑖 3 Hankel-H-2-Bessel-third-kind 2 3 𝜁 superscript 𝑒 𝜋 𝑖 6 3 𝑧 diffop Airy-Ai 1 𝑧 𝑖 diffop Airy-Bi 1 𝑧 {\displaystyle{\displaystyle{H^{(2)}_{2/3}}\left(\zeta\right)=e^{2\pi i/3}{H^{% (2)}_{-2/3}}\left(\zeta\right)=e^{-\pi i/6}(\sqrt{3}/z)\left(\mathrm{Ai}'\left% (-z\right)+i\mathrm{Bi}'\left(-z\right)\right).}}
    0 references
    DLMF id
    DLMF:9.6.E20
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1amdec
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    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2akdec
    0 references
    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.m2aidec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2amdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2akdec
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    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1sdec
    0 references
    change of variable (locally)
    Defining formula
    ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    xml-id
    C9.S6.XMD2.m1jdec
    0 references
     
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