Formula:1785

Digital Library of Mathematical Functions ID 4.13.E11

${\displaystyle{\displaystyle\mathrm{Wm}\left(x\right)=-\eta-\ln\eta-\frac{\ln\eta}{\eta}-\frac{(\ln\eta)^{2}}{2\eta^{2}}-\frac{\ln\eta}{\eta^{2}}+O\left(\frac{(\ln\eta)^{3}}{\eta^{3}}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\mathrm{Wm}\left(\NVar{x}\right)}}$: nonprincipal branch of Lambert W -function
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\eta}}$: η
 

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