DLMF:9.8.E23 (Q2858)

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DLMF:9.8.E23
No description defined

    Statements

    Defining formula
    ϕ ⁡ ( x ) ∼ - π 4 + 2 3 ⁢ ( - x ) 3 / 2 ⁢ ( 1 - 7 32 ⁢ 1 x 3 - 1463 6144 ⁢ 1 x 6 - 4 95271 3 27680 ⁢ 1 x 9 - 2065 30429 83 88608 ⁢ 1 x 12 - ⋯ ) . asymptotic-expansion phase-Airy-Phi 𝑥 𝜋 4 2 3 superscript 𝑥 3 2 1 7 32 1 superscript 𝑥 3 1463 6144 1 superscript 𝑥 6 4 95271 3 27680 1 superscript 𝑥 9 2065 30429 83 88608 1 superscript 𝑥 12 ⋯ {\displaystyle{\displaystyle\phi\left(x\right)\sim-\frac{\pi}{4}+\frac{2}{3}(-% x)^{3/2}\left(1-\frac{7}{32}\frac{1}{x^{3}}-\frac{1463}{6144}\frac{1}{x^{6}}-% \frac{4\;95271}{3\;27680}\frac{1}{x^{9}}-\frac{2065\;30429}{83\;88608}\frac{1}% {x^{12}}-\cdots\right).}}
    0 references
    DLMF id
    DLMF:9.8.E23
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    Airy phase function
    Defining formula
    ϕ ⁡ ( z ) phase-Airy-Phi 𝑧 {\displaystyle{\displaystyle\phi\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E8.m2ahdec
    0 references
    Q11382
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S1.XMD2.m1vdec
    0 references
     
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