DLMF:2.3.E4 (Q720): Difference between revisions

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

x\to+\infty
Property / constraint: x + 𝑥 {\displaystyle{\displaystyle x\to+\infty}} / rank
 
Normal rank

Revision as of 16:52, 30 December 2019

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DLMF:2.3.E4
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    a b e i x t q ( t ) d t e i a x s = 0 q ( s ) ( a ) ( i x ) s + 1 - e i b x s = 0 q ( s ) ( b ) ( i x ) s + 1 , asymptotic-expansion superscript subscript 𝑎 𝑏 superscript 𝑒 𝑖 𝑥 𝑡 𝑞 𝑡 𝑡 superscript 𝑒 𝑖 𝑎 𝑥 superscript subscript 𝑠 0 superscript 𝑞 𝑠 𝑎 superscript 𝑖 𝑥 𝑠 1 superscript 𝑒 𝑖 𝑏 𝑥 superscript subscript 𝑠 0 superscript 𝑞 𝑠 𝑏 superscript 𝑖 𝑥 𝑠 1 {\displaystyle{\displaystyle\int_{a}^{b}e^{ixt}q(t)\mathrm{d}t\sim e^{iax}\sum% _{s=0}^{\infty}q^{(s)}(a)\left(\frac{i}{x}\right)^{s+1}-e^{ibx}\sum_{s=0}^{% \infty}q^{(s)}(b)\left(\frac{i}{x}\right)^{s+1},}}
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    DLMF:2.3.E4
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    x + 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
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