DLMF:9.12.E19 (Q2947): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11382 / rank
 
Normal rank
Property / Symbols used: Q11382 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11382 / qualifier
 
xml-id: C9.S1.XMD2.m1bdec

Latest revision as of 14:55, 2 January 2020

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DLMF:9.12.E19
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    Statements

    Defining formula
    Gi ⁡ ( x ) = 1 π ⁢ ∫ 0 ∞ sin ⁡ ( 1 3 ⁢ t 3 + x ⁢ t ) ⁢ d t , Scorer-Gi 𝑥 1 𝜋 superscript subscript 0 1 3 superscript 𝑡 3 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{Gi}\left(x\right)=\frac{1}{\pi}\int_{0}^{% \infty}\sin\left(\tfrac{1}{3}t^{3}+xt\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:9.12.E19
    0 references
    constraint
    x ∈ ℝ 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}
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    Symbols used
    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.m2akdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aldec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q10812
    Defining formula
    ℝ {\displaystyle{\displaystyle\mathbb{R}}}
    xml-id
    introduction.Sx4.p2.t1.r14.m2adec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q11382
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S1.XMD2.m1bdec
    0 references
     
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