2.3.E4

MaRDI QIDQ690

• Label: 2.3.E4

Digital Library of Mathematical Functions ID 2.3.E4

${\displaystyle{\displaystyle\int_{a}^{b}e^{ixt}q(t)\mathrm{d}t\sim e^{iax}\sum_{s=0}^{\infty}q^{(s)}(a)\left(\frac{i}{x}\right)^{s+1}-e^{ibx}\sum_{s=0}^{\infty}q^{(s)}(b)\left(\frac{i}{x}\right)^{s+1},}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle q(t)}}$: infinitely differentiable function
• ${\displaystyle{\displaystyle a}}$: left endpoint
• ${\displaystyle{\displaystyle b}}$: right endpoint
 

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