DLMF:9.11.E14 (Q2921)

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DLMF:9.11.E14
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    Statements

    Defining formula
    ∫ Ai ⁡ ( z ) ⁢ Bi ⁡ ( z ) ( Ai 2 ⁡ ( z ) + Bi 2 ⁡ ( z ) ) 2 ⁢ d z = π 2 ⁢ Bi 2 ⁡ ( z ) Ai 2 ⁡ ( z ) + Bi 2 ⁡ ( z ) . Airy-Ai 𝑧 Airy-Bi 𝑧 superscript Airy-Ai 2 𝑧 Airy-Bi 2 𝑧 2 𝑧 𝜋 2 Airy-Bi 2 𝑧 Airy-Ai 2 𝑧 Airy-Bi 2 𝑧 {\displaystyle{\displaystyle\int\frac{\mathrm{Ai}\left(z\right)\mathrm{Bi}% \left(z\right)}{\left({\mathrm{Ai}^{2}}\left(z\right)+{\mathrm{Bi}^{2}}\left(z% \right)\right)^{2}}\mathrm{d}z=\frac{\pi}{2}\frac{{\mathrm{Bi}^{2}}\left(z% \right)}{{\mathrm{Ai}^{2}}\left(z\right)+{\mathrm{Bi}^{2}}\left(z\right)}.}}
    0 references
    DLMF id
    DLMF:9.11.E14
    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.m1aedec
    0 references
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
     
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