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Walter Gautschi, Volume 1 pp 41–48Cite as

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Special functions

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Part of the book series: Contemporary Mathematicians ((CM))

Abstract

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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Authors and Affiliations

  1. Departamento de Matematicas, Universidad de Cantabria, 39005, Santander, SPAIN

    Javier Segura

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  1. Javier Segura
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Editors and Affiliations

  1. Villeneuve d’Ascq, France

    Claude Brezinski

  2. Department of Computer Science, Purdue University, West Lafayette, Indiana, USA

    Ahmed Sameh

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Segura, J. (2014). Special functions. In: Brezinski, C., Sameh, A. (eds) Walter Gautschi, Volume 1. Contemporary Mathematicians. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7034-2_6

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