Abstract
In this article the solution procedure is formulated when the Frobenius method is applied to the equations of motion for incipient buoyant thermal convection in vertical cylindrical geometries. The indicial equation associated with the resulting sixth-order linear ordinary differential equation has four roots, two of which are repeated and all of which differ by the same integer. The resulting solution suggests a decomposition of the sixth-order equation into three second-order equations. The solution and decomposition procedure is then expanded to equations of nth order.
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