DLMF:9.2.E15 (Q2767)

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DLMF:9.2.E15
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    Statements

    Defining formula
    Bi ⁡ ( - z ) = e - π ⁢ i / 6 ⁢ Ai ⁡ ( z ⁢ e π ⁢ i / 3 ) + e π ⁢ i / 6 ⁢ Ai ⁡ ( z ⁢ e - π ⁢ i / 3 ) . Airy-Bi 𝑧 superscript 𝑒 𝜋 𝑖 6 Airy-Ai 𝑧 superscript 𝑒 𝜋 𝑖 3 superscript 𝑒 𝜋 𝑖 6 Airy-Ai 𝑧 superscript 𝑒 𝜋 𝑖 3 {\displaystyle{\displaystyle\mathrm{Bi}\left(-z\right)=e^{-\pi i/6}\mathrm{Ai}% \left(ze^{\pi i/3}\right)+e^{\pi i/6}\mathrm{Ai}\left(ze^{-\pi i/3}\right).}}
    0 references
    DLMF id
    DLMF:9.2.E15
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    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1akdec
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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.m2ahdec
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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.m2ajdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aidec
    0 references
     
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