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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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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DOI: https://doi.org/10.1007/978-1-4614-7034-2_6
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