  Recently there has been progress in the computation of the anomalous
dimensions of gauge theory operators at strong coupling by making use of
AdS/CFT correspondence. On string theory side they are given by dispersion
relations in the semiclassical regime. We revisit the problem of large charges
expansion of the dispersion relations for simple semiclassical strings in
$AdS_4\times\mathbb{CP}^3$ background. We present the calculation of the
corresponding anomalous dimensions of the gauge theory operators to an
arbitrary order using three different methods. Although the results of the
three methods look different, power series expansions show their consistency.
