DLMF:12.14.E35 (Q4277): Difference between revisions

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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.m11ajdec

Revision as of 15:32, 2 January 2020

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DLMF:12.14.E35
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    Statements

    Defining formula
    W ′ ⁡ ( - 1 2 ⁢ μ 2 , μ ⁢ t ⁢ 2 ) ∼ - μ 2 ⁢ l ⁢ ( μ ) ⁢ ( t 2 + 1 ) 1 4 ⁢ ( sin ⁡ σ ¯ ⁢ ∑ s = 0 ∞ ( - 1 ) s ⁢ v ¯ 2 ⁢ s ⁢ ( t ) ( t 2 + 1 ) 3 ⁢ s ⁢ μ 4 ⁢ s + cos ⁡ σ ¯ ⁢ ∑ s = 0 ∞ ( - 1 ) s ⁢ v ¯ 2 ⁢ s + 1 ⁢ ( t ) ( t 2 + 1 ) 3 ⁢ s + 3 2 ⁢ μ 4 ⁢ s + 2 ) , asymptotic-expansion diffop parabolic-W 1 1 2 superscript 𝜇 2 𝜇 𝑡 2 𝜇 2 𝑙 𝜇 superscript superscript 𝑡 2 1 1 4 ¯ 𝜎 superscript subscript 𝑠 0 superscript 1 𝑠 subscript ¯ 𝑣 2 𝑠 𝑡 superscript superscript 𝑡 2 1 3 𝑠 superscript 𝜇 4 𝑠 ¯ 𝜎 superscript subscript 𝑠 0 superscript 1 𝑠 subscript ¯ 𝑣 2 𝑠 1 𝑡 superscript superscript 𝑡 2 1 3 𝑠 3 2 superscript 𝜇 4 𝑠 2 {\displaystyle{\displaystyle W'\left(-\tfrac{1}{2}\mu^{2},\mu t\sqrt{2}\right)% \sim-\frac{\mu}{\sqrt{2}}l(\mu)(t^{2}+1)^{\frac{1}{4}}\left(\sin\overline{% \sigma}\sum_{s=0}^{\infty}\frac{(-1)^{s}\overline{v}_{2s}(t)}{(t^{2}+1)^{3s}% \mu^{4s}}+\cos\overline{\sigma}\sum_{s=0}^{\infty}\frac{(-1)^{s}\overline{v}_{% 2s+1}(t)}{(t^{2}+1)^{3s+\frac{3}{2}}\mu^{4s+2}}\right),}}
    0 references
    DLMF id
    DLMF:12.14.E35
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11ajdec
    0 references
     
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