DLMF:9.11.E13 (Q2920)

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DLMF:9.11.E13
No description defined

    Statements

    Defining formula
    ∫ d z Ai ⁡ ( z ) ⁢ Bi ⁡ ( z ) = π ⁢ ln ⁡ ( Bi ⁡ ( z ) Ai ⁡ ( z ) ) , 𝑧 Airy-Ai 𝑧 Airy-Bi 𝑧 𝜋 Airy-Bi 𝑧 Airy-Ai 𝑧 {\displaystyle{\displaystyle\int\frac{\mathrm{d}z}{\mathrm{Ai}\left(z\right)% \mathrm{Bi}\left(z\right)}=\pi\ln\left(\frac{\mathrm{Bi}\left(z\right)}{% \mathrm{Ai}\left(z\right)}\right),}}
    0 references
    DLMF id
    DLMF:9.11.E13
    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.m1addec
    0 references
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1kdec
    0 references
     
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