Formula:702

Digital Library of Mathematical Functions ID 2.3.E15

${\displaystyle{\displaystyle\int_{a}^{b}e^{-xp(t)}q(t)\mathrm{d}t\sim e^{-xp(a)}\sum_{s=0}^{\infty}\Gamma\left(\frac{s+\lambda}{\mu}\right)\frac{b_{s}}{x^{(s+\lambda)/\mu}},}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle a}}$: left endpoint
• ${\displaystyle{\displaystyle b}}$: right endpoint
• ${\displaystyle{\displaystyle p(t)}}$: real function
• ${\displaystyle{\displaystyle q(t)}}$: function
• ${\displaystyle{\displaystyle\lambda}}$: positive constant
• ${\displaystyle{\displaystyle\mu}}$: positive constant
 

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