DLMF:12.10.E35 (Q4200): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11andec

Revision as of 15:21, 2 January 2020

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DLMF:12.10.E35
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    Statements

    Defining formula
    U ⁡ ( - 1 2 ⁢ μ 2 , μ ⁢ t ⁢ 2 ) ∼ 2 ⁢ π 1 2 ⁢ μ 1 3 ⁢ g ⁢ ( μ ) ⁢ ϕ ⁢ ( ζ ) ⁢ ( Ai ⁡ ( μ 4 3 ⁢ ζ ) ⁢ ∑ s = 0 ∞ A s ⁢ ( ζ ) μ 4 ⁢ s + Ai ′ ⁡ ( μ 4 3 ⁢ ζ ) μ 8 3 ⁢ ∑ s = 0 ∞ B s ⁢ ( ζ ) μ 4 ⁢ s ) , asymptotic-expansion parabolic-U 1 2 superscript 𝜇 2 𝜇 𝑡 2 2 superscript 𝜋 1 2 superscript 𝜇 1 3 𝑔 𝜇 italic-ϕ 𝜁 Airy-Ai superscript 𝜇 4 3 𝜁 superscript subscript 𝑠 0 subscript 𝐴 𝑠 𝜁 superscript 𝜇 4 𝑠 diffop Airy-Ai 1 superscript 𝜇 4 3 𝜁 superscript 𝜇 8 3 superscript subscript 𝑠 0 subscript 𝐵 𝑠 𝜁 superscript 𝜇 4 𝑠 {\displaystyle{\displaystyle U\left(-\frac{1}{2}\mu^{2},\mu t\sqrt{2}\right)% \sim 2\pi^{\frac{1}{2}}\mu^{\frac{1}{3}}g(\mu)\phi(\zeta)\*\left(\mathrm{Ai}% \left(\mu^{\frac{4}{3}}\zeta\right)\sum_{s=0}^{\infty}\frac{A_{s}(\zeta)}{\mu^% {4s}}+\frac{\mathrm{Ai}'\left(\mu^{\frac{4}{3}}\zeta\right)}{\mu^{\frac{8}{3}}% }\sum_{s=0}^{\infty}\frac{B_{s}(\zeta)}{\mu^{4s}}\right),}}
    0 references
    DLMF id
    DLMF:12.10.E35
    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.m1adec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11andec
    0 references
     
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