Formula:687

Digital Library of Mathematical Functions ID 2.3.E2

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-xt}q(t)\mathrm{d}t\sim\sum_{s=0}^{\infty}\frac{q^{(s)}(0)}{x^{s+1}},}}$

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
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle q(t)}}$: infinitely differentiable function
 

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