\begin{document}$ W^{\pm}+X \rightarrow e^{\pm} \nu +X $\end{document} production in proton-proton (pp) collisions. Perturbative QCD calculations are performed at next-to-next-to-leading order (NNLO) accuracy using different parton distribution function (PDF) models at 8, 13, and 14 TeV center-of-mass energies of CERN LHC pp collisions. NNLO calculations are performed for electrons with transverse momenta above 20 GeV in the forward electron pseudorapidity region \begin{document}$ 2.0 \leqslant \eta_{e} \leqslant 4.25 $\end{document}. NNLO predictions are first compared at 8 TeV with the measurements of the LHCb experiment at the LHC for the \begin{document}$ W^{+} $\end{document}/\begin{document}$ W^{-} $\end{document} cross section ratio and charge asymmetry distributions. The 8 TeV predictions using NNPDF3.1, CT14, and MMHT2014 PDF sets are reported to be in good agreement with the LHCb data for the entire \begin{document}$ \eta_{e} $\end{document} region, justifying the extension of the calculations to 13 and 14 TeV energies. The charge asymmetry predictions at NNLO accuracy are reported in the forward \begin{document}$ \eta_{e} $\end{document} bins at 13 and 14 TeV and compared among NNPDF3.1, CT14, and MMHT2014 PDF sets. Overall, the predicted \begin{document}$ W^{\pm} $\end{document} differential cross-section and charge asymmetry distributions based on different PDF sets are found to be consistent with each other for the entire \begin{document}$ \eta_{e} $\end{document} region. The charge asymmetry distributions are shown to be more sensitive to discriminate among different PDF models in terms of the 14 TeV predictions."> NNLO QCD predictions of electron charge asymmetry for inclusive <i>pp</i> → <i>W</i> + <i>X</i> production in forward region at 13 and 14 TeV -
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