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