DLMF:2.3.E15 (Q732): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2abdec

Revision as of 15:52, 1 January 2020

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DLMF:2.3.E15
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    Statements

    test
    ∫ a b e - x ⁢ p ⁢ ( t ) ⁢ q ⁢ ( t ) ⁢ d t ∼ e - x ⁢ p ⁢ ( a ) ⁢ ∑ s = 0 ∞ Γ ⁡ ( s + λ μ ) ⁢ b s x ( s + λ ) / μ , asymptotic-expansion superscript subscript 𝑎 𝑏 superscript 𝑒 𝑥 𝑝 𝑡 𝑞 𝑡 𝑡 superscript 𝑒 𝑥 𝑝 𝑎 superscript subscript 𝑠 0 Euler-Gamma 𝑠 𝜆 𝜇 subscript 𝑏 𝑠 superscript 𝑥 𝑠 𝜆 𝜇 {\displaystyle{\displaystyle\int_{a}^{b}e^{-xp(t)}q(t)\mathrm{d}t\sim e^{-xp(a% )}\sum_{s=0}^{\infty}\Gamma\left(\frac{s+\lambda}{\mu}\right)\frac{b_{s}}{x^{(% s+\lambda)/\mu}},}}
    0 references
    DLMF id
    DLMF:2.3.E15
    0 references
    constraint
    x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
     
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