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A method is presented (with standard examples) based on an elementary complex integral expression, for developing Frobenius series solutions for second-order linear homogeneous ordinary Fuchs differential equations. The method reduces the task of finding a series solution to the solution, instead, of a system of simple equations in a single variable. The method is straightforward to apply as an algorithm, and eliminates the manipulation of power series, so characteristic of the usual approach [14]. The method is a generalization of a procedure developed by Herrera [4] for finding Maclaurin series solutions for nonlinear differential equations.Mathematics Subject Classification: 30B10, 30E20 34A25, 34A30

A method is presented, with standard examples, based on an elementary complex integral expression, for developing, in particular, series solutions for second-order linear homogeneous ordinary differential equations. Straightforward to apply, the method reduces the task of finding a series solution to the solution, instead, of a system of simple equations in a single variable. The method eliminates the need to manipulate power series and balance powers, which is a characteristic of the usual approach. The method originated with Herrera [3], but was applied to the solution of certain classes of nonlinear ordinary differential equations by him.Mathematics Subject Classification: 30B10, 30E20 34A25, 34A30

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In this paper, we present a new systematic approach to the solution of the hypergeometric-like differential equation and its associated equation. The method produces, tout court, the general solution of these equations in the form of a combination of a standard Rodrigues formula and a 'generalized' Rodrigues formula, of a type due originally to Gonçalves [5] and recently considered, again, by Area et al [1]. In addition, a novel analysis of a class of integrals determining the generalized Rodrigues formulae is given, which complements an original analysis of Area et al [1]. Finally, the relation between the hypergeometric-type differential equation and the hypergeometric equation is elucidated further, following the work of Koepf and Masjed-Jamel [7]. Mathematics Subject Classification: 33C25; 33C45