DLMF:9.7.E10 (Q2817): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2agdec

Revision as of 14:33, 2 January 2020

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DLMF:9.7.E10
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    Statements

    Defining formula
    Ai ′ ⁡ ( - z ) ∼ z 1 / 4 π ⁢ ( sin ⁡ ( ζ - 1 4 ⁢ π ) ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ v 2 ⁢ k ζ 2 ⁢ k - cos ⁡ ( ζ - 1 4 ⁢ π ) ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ v 2 ⁢ k + 1 ζ 2 ⁢ k + 1 ) , asymptotic-expansion diffop Airy-Ai 1 𝑧 superscript 𝑧 1 4 𝜋 𝜁 1 4 𝜋 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑣 2 𝑘 superscript 𝜁 2 𝑘 𝜁 1 4 𝜋 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑣 2 𝑘 1 superscript 𝜁 2 𝑘 1 {\displaystyle{\displaystyle\mathrm{Ai}'\left(-z\right)\sim\frac{z^{1/4}}{% \sqrt{\pi}}\left(\sin\left(\zeta-\tfrac{1}{4}\pi\right)\sum_{k=0}^{\infty}(-1)% ^{k}\frac{v_{2k}}{\zeta^{2k}}-\cos\left(\zeta-\tfrac{1}{4}\pi\right)\sum_{k=0}% ^{\infty}(-1)^{k}\frac{v_{2k+1}}{\zeta^{2k+1}}\right),}}
    0 references
    DLMF id
    DLMF:9.7.E10
    0 references
    constraint
    | ph ⁡ z | ≤ 2 3 ⁢ π - δ phase 𝑧 2 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{2}{3}\pi-\delta}}
    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.m1acdec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
    0 references
     
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