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Strength and Weakness of Three-Term Recurrence Relations

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Alcune questioni di analisi numerica

Part of the book series: C.I.M.E. Summer Schools ((CIME,volume 35))

Abstract

The expression “three-term recurrence relation,” as used here, is meant to be synonymous with “second-order linear difference equation.” We are thus considering relations of the form

$$y_{n + 1} + a_n y_n + b_n y_{n-1} = 0$$
((0.1))

We assume that an and bn are given real or complex-valued functions, defined on the set of positive integers, and regard yn as the unknown function, with its domain being the set of non-negative integers. Relation (0.1) is required, then, to hold for n = 1,2,3,…(1′)

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Authors
  1. Walter Gautschi
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Aldo Ghizzetti (Coordinatore)

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Gautschi, W. (2010). Strength and Weakness of Three-Term Recurrence Relations. In: Ghizzetti, A. (eds) Alcune questioni di analisi numerica. C.I.M.E. Summer Schools, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11027-6_3

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