DLMF:12.10.E21 (Q4183): Difference between revisions

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‎Changed an Item: Add constraint
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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.m11aidec

Revision as of 15:19, 2 January 2020

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DLMF:12.10.E21
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    Statements

    Defining formula
    V ′ ⁡ ( - 1 2 ⁢ μ 2 , μ ⁢ t ⁢ 2 ) ∼ μ ⁢ 2 ⁢ g ⁢ ( μ ) ⁢ ( 1 - t 2 ) 1 4 Γ ⁡ ( 1 2 + 1 2 ⁢ μ 2 ) ⁢ ( sin ⁡ χ ⁢ ∑ s = 0 ∞ ( - 1 ) s ⁢ ℬ ~ 2 ⁢ s ⁢ ( t ) μ 4 ⁢ s + cos ⁡ χ ⁢ ∑ s = 0 ∞ ( - 1 ) s ⁢ ℬ ~ 2 ⁢ s + 1 ⁢ ( t ) μ 4 ⁢ s + 2 ) , asymptotic-expansion diffop parabolic-V 1 1 2 superscript 𝜇 2 𝜇 𝑡 2 𝜇 2 𝑔 𝜇 superscript 1 superscript 𝑡 2 1 4 Euler-Gamma 1 2 1 2 superscript 𝜇 2 𝜒 superscript subscript 𝑠 0 superscript 1 𝑠 subscript ~ ℬ 2 𝑠 𝑡 superscript 𝜇 4 𝑠 𝜒 superscript subscript 𝑠 0 superscript 1 𝑠 subscript ~ ℬ 2 𝑠 1 𝑡 superscript 𝜇 4 𝑠 2 {\displaystyle{\displaystyle V'\left(-\tfrac{1}{2}\mu^{2},\mu t\sqrt{2}\right)% \sim\frac{\mu\sqrt{2}g(\mu)(1-t^{2})^{\frac{1}{4}}}{\Gamma\left(\tfrac{1}{2}+% \tfrac{1}{2}\mu^{2}\right)}\*\left(\sin\chi\sum_{s=0}^{\infty}(-1)^{s}\frac{% \widetilde{\cal{B}}_{2s}(t)}{\mu^{4s}}+\cos\chi\sum_{s=0}^{\infty}(-1)^{s}% \frac{\widetilde{\cal{B}}_{2s+1}(t)}{\mu^{4s+2}}\right),}}
    0 references
    DLMF id
    DLMF:12.10.E21
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aidec
    0 references
     
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