Formula:695

Digital Library of Mathematical Functions ID 2.3.E9

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-xt}q(t)\ln t\mathrm{d}t\sim\sum_{s=0}^{\infty}\Gamma'\left(\frac{s+\lambda}{\mu}\right)\frac{a_{s}}{x^{(s+\lambda)/\mu}}-(\ln x)\sum_{s=0}^{\infty}\Gamma\left(\frac{s+\lambda}{\mu}\right)\frac{a_{s}}{x^{(s+\lambda)/\mu}},}}$

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
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle a}}$: positive constant
• ${\displaystyle{\displaystyle q(t)}}$: function (locally)
• ${\displaystyle{\displaystyle\lambda}}$: positive constant
• ${\displaystyle{\displaystyle\mu}}$: positive constant
 

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