The Solution of a System of Linear Differential Equations With a Regular Singular Point: A Thesis (Classic Reprint)

This book tackles the problem of finding fundamental sets of solutions for systems of linear differential equations possessing regular singular points. A fundamental set is a set of solutions such that every solution of the system can be expressed as a linear combination of the elements of that set. Any subset of a linearly independent set of solutions forms a fundamental set. The problem was first investigated by Fuchs in 1891. The book uses methods developed by Nyawandor, and considers the case of two independent variables, and hence two equations. The author provides three cases to consider, depending on the relationship between the roots of the indicial equation, and discusses the solutions for each case. The book concludes with a discussion of the linear independence of the solutions and their significance within the broader context of the theory of linear differential equations.