DLMF:9.10.E6 (Q2888): Difference between revisions

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Property / constraint
 

x - 𝑥 {\displaystyle{\displaystyle x\rightarrow-\infty}}

x\rightarrow-\infty
Property / constraint: x - 𝑥 {\displaystyle{\displaystyle x\rightarrow-\infty}} / rank
 
Normal rank

Revision as of 16:13, 30 December 2019

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DLMF:9.10.E6
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    Statements

    - x Ai ( t ) d t = π - 1 / 2 ( - x ) - 3 / 4 cos ( 2 3 ( - x ) 3 / 2 + 1 4 π ) + O ( | x | - 9 / 4 ) , superscript subscript 𝑥 Airy-Ai 𝑡 𝑡 superscript 𝜋 1 2 superscript 𝑥 3 4 2 3 superscript 𝑥 3 2 1 4 𝜋 Big-O superscript 𝑥 9 4 {\displaystyle{\displaystyle\int_{-\infty}^{x}\mathrm{Ai}\left(t\right)\mathrm% {d}t=\pi^{-1/2}(-x)^{-3/4}\*\cos\left(\tfrac{2}{3}(-x)^{3/2}+\tfrac{1}{4}\pi% \right)+O\left(|x|^{-9/4}\right),}}
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    x - 𝑥 {\displaystyle{\displaystyle x\rightarrow-\infty}}
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