Abstract
<abstract> In this paper, the local integrability of a class of three-dimensional systems is studied. The recursive formulas to compute the generalized focus quantities of the system are deduced firstly, then they are applied to a Lotka-Volterra system. The integrable conditions of the system are obtained and the local integrability is solved completely. The algorithm corresponding to the above formulas is an extension and development of the power series method for the planar differential systems with $ p:-q $ arbitrary resonant saddle point and also readily done with using computer algebra system such as Mathematica or Maple. </abstract>
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