Summary of the Frobenius Method

The examples selected and the discussion of convergence properties focused on solutions around the point jeg = 0. This is the usual case for chemical engineering transport processes, since cylindrical or spherical geometry usually includes the origin as part of the solution domain. There are exceptions, of course, for example, annular flow in a cylindrical pipe. For the exceptional case, series solutions can always be undertaken for finite Xq expressed as powers of (x - Xg), which simply implies a shift of the origin. 

we have shown that any second (or higher) order, variable coefficient equation of the type 

The indicial equation was found by inspecting the coefficients of the lowest 

The recurrence relation was found by progressively removing terms and 

Three general cases would arise on inspecting the character of the roots 

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