Formula:739

Digital Library of Mathematical Functions ID 2.4.E15

${\displaystyle{\displaystyle\int_{a}^{b}e^{-zp(t)}q(t)\mathrm{d}t\sim 2e^{-zp(t_{0})}\sum_{s=0}^{\infty}\Gamma\left(s+\tfrac{1}{2}\right)\frac{b_{2s}}{z^{s+(1/2)}},}}$

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
• ${\displaystyle{\displaystyle p(t)}}$: analytic function
• ${\displaystyle{\displaystyle q(t)}}$: analytic function
 

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