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DLMF:9.6.E16 - MaRDI portal

DLMF:9.6.E16 (Q3494)

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DLMF:9.6.E16
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    Statements

    DLMF defining formula
    K ± 2 / 3 ⁡ ( ζ ) = - π ⁢ ( 3 / z ) ⁢ Ai ′ ⁡ ( z ) , modified-Bessel-second-kind plus-or-minus 2 3 𝜁 𝜋 3 𝑧 diffop Airy-Ai 1 𝑧 {\displaystyle{\displaystyle K_{\pm 2/3}\left(\zeta\right)=-\pi(\sqrt{3}/z)% \mathrm{Ai}'\left(z\right),}}
    0 references
    Symbols used
    Q10893
    DLMF defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1aidec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    modified Bessel function of the second kind
    DLMF defining formula
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1odec
    0 references
    change of variable (locally)
    DLMF defining formula
    ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    xml-id
    C9.S6.XMD2.m1fdec
    0 references
     
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