Special functions

  • Javier Segura
Part of the Contemporary Mathematicians book series (CM)


The collection of papers by Walter Gautschi dealing with special functions has, of course, connections with other sections in these volumes. First, we have to mention the article [GA29], which is included in Section 14 dedicated to difference equations, where the conditioning of three-term recurrence relations is analyzed and methods of computation using recurrence relations are developed; for a more recent review, see [GA150]. Recurrence relations are basic tools for computing special functions, particularly functions of hypergeometric type. In [GA29], also the relation between the existence of a minimal solution for the recurrence and the convergence of the associated continued fraction is discussed. Reference [GA29] is a pioneering and influential paper in the field of special functions, and it is a highly cited paper (316 citations as of now).


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Javier Segura
    • 1
  1. 1.Departamento de MatematicasUniversidad de CantabriaSantanderSPAIN

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