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DLMF:9.2.E14 - MaRDI portal

DLMF:9.2.E14 (Q3464)

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DLMF:9.2.E14
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    Statements

    Ai ( - z ) = e π i / 3 Ai ( z e π i / 3 ) + e - π i / 3 Ai ( z e - π i / 3 ) , Airy-Ai 𝑧 superscript 𝑒 𝜋 𝑖 3 Airy-Ai 𝑧 superscript 𝑒 𝜋 𝑖 3 superscript 𝑒 𝜋 𝑖 3 Airy-Ai 𝑧 superscript 𝑒 𝜋 𝑖 3 {\displaystyle{\displaystyle\mathrm{Ai}\left(-z\right)=e^{\pi i/3}\mathrm{Ai}% \left(ze^{\pi i/3}\right)+e^{-\pi i/3}\mathrm{Ai}\left(ze^{-\pi i/3}\right),}}
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    Ai ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    C9.S2.SS1.m1ajdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aidec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2ahdec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2ahdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C9.S1.XMD3.m1jdec
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    Identifiers