Physics – Mathematical Physics
Scientific paper
2004-02-16
Physics
Mathematical Physics
9 pages, related to math.GM/0002059, submitted for publication in the European Journal of Applied Mathematics, see also http
Scientific paper
In a recent paper, a new 3-parameter class of Abel type equations, so-called AIR, all of whose members can be mapped into Riccati equations, is shown. Most of the Abel equations with solution presented in the literature belong to the AIR class. Three canonical forms were shown to generate this class, according to the roots of a cubic. In this paper, a connection between those canonical forms and the differential equations for the hypergeometric functions 2F1, 1F1 and 0F1 is unveiled. This connection provides a closed form pFq solution for all Abel equations of the AIR class.
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