The elliptic flow, $v_{2}$, of muons from heavy-flavour hadron decays at forward rapidity ($2.5 < y < 4$) is measured in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$~=~2.76 TeV with the ALICE detector at the LHC. The scalar product, two- and four-particle $Q$ cumulants and Lee-Yang zeros methods are used. The dependence of the $v_2$ of muons from heavy-flavour hadron decays on the collision centrality, in the range 0--40\%, and on transverse momentum, $p_{\rm T}$, is studied in the interval $3 < p_{\rm T} < 10$~GeV/$c$. A positive $v_2$ is observed with the scalar product and two-particle $Q$ cumulants in semi-central collisions (10--20\% and 20--40\% centrality classes) for the $p_{\rm T}$ interval from 3 to about 5 GeV/$c$. The $v_2$ magnitude tends to decrease towards more central collisions and with increasing $p_{\rm T}$. It becomes compatible with zero in the interval $6<p_{\rm T}<10~{\rm GeV/}c$. The results are compared to models describing the interaction of heavy quarks and open heavy-flavour hadrons with the high-density medium formed in high-energy heavy-ion collisions. The model calculations describe the measured $v_2$ within uncertainties.
pT-differential inclusive muon $v_{2}$ extracted with scalar product method.
pT-differential inclusive muon $v_{2}$ extracted with two-particle $Q$ cumulants method.
pT-differential inclusive muon $v_{2}$ extracted with scalar product method.
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