DLMF:2.3.E8 (Q724): Difference between revisions

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Property / constraint
 

x + 𝑥 {\displaystyle{\displaystyle x\to+\infty}}

x\to+\infty
Property / constraint: x + 𝑥 {\displaystyle{\displaystyle x\to+\infty}} / rank
 
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Revision as of 15:52, 30 December 2019

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DLMF:2.3.E8
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    0 e - x t q ( t ) d t s = 0 Γ ( s + λ μ ) a s x ( s + λ ) / μ , asymptotic-expansion superscript subscript 0 superscript 𝑒 𝑥 𝑡 𝑞 𝑡 𝑡 superscript subscript 𝑠 0 Euler-Gamma 𝑠 𝜆 𝜇 subscript 𝑎 𝑠 superscript 𝑥 𝑠 𝜆 𝜇 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-xt}q(t)\mathrm{d}t\sim\sum_{s% =0}^{\infty}\Gamma\left(\frac{s+\lambda}{\mu}\right)\frac{a_{s}}{x^{(s+\lambda% )/\mu}},}}
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    x + 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
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