DLMF:9.10.E3 (Q2885)

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DLMF:9.10.E3
No description defined

    Statements

    Defining formula
    ∫ - ∞ z Bi ⁡ ( t ) ⁢ d t = ∫ 0 z Bi ⁡ ( t ) ⁢ d t = π ⁢ ( Bi ′ ⁡ ( z ) ⁢ Gi ⁡ ( z ) - Bi ⁡ ( z ) ⁢ Gi ′ ⁡ ( z ) ) = π ⁢ ( Bi ⁡ ( z ) ⁢ Hi ′ ⁡ ( z ) - Bi ′ ⁡ ( z ) ⁢ Hi ⁡ ( z ) ) . superscript subscript 𝑧 Airy-Bi 𝑡 𝑡 superscript subscript 0 𝑧 Airy-Bi 𝑡 𝑡 𝜋 diffop Airy-Bi 1 𝑧 Scorer-Gi 𝑧 Airy-Bi 𝑧 diffop Scorer-Gi 1 𝑧 𝜋 Airy-Bi 𝑧 diffop Scorer-Hi 1 𝑧 diffop Airy-Bi 1 𝑧 Scorer-Hi 𝑧 {\displaystyle{\displaystyle\int_{-\infty}^{z}\mathrm{Bi}\left(t\right)\mathrm% {d}t=\int_{0}^{z}\mathrm{Bi}\left(t\right)\mathrm{d}t=\pi\left(\mathrm{Bi}'% \left(z\right)\mathrm{Gi}\left(z\right)-\mathrm{Bi}\left(z\right)\mathrm{Gi}'% \left(z\right)\right)\\ =\pi\left(\mathrm{Bi}\left(z\right)\mathrm{Hi}'\left(z\right)-\mathrm{Bi}'% \left(z\right)\mathrm{Hi}\left(z\right)\right).}}
    0 references
    DLMF id
    DLMF:9.10.E3
    0 references
    Symbols used
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2adec
    0 references
    Scorer function (inhomogeneous Airy function)
    Defining formula
    Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E4.m2aadec
    0 references
    Scorer function (inhomogeneous Airy function)
    Defining formula
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1bdec
    0 references
     
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