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Stability of Roots of Polynomials Under Linear Combinations of Derivatives

✍ Scribed by Branko Ćurgus; Vania Mascioni

Book ID
106045784
Publisher
Springer
Year
2009
Tongue
English
Weight
533 KB
Volume
32
Category
Article
ISSN
0176-4276

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When do linear combinations of orthogona
When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?
✍ Manuel Alfaro; Francisco Marcellán; Ana Peña; M. Luisa Rezola 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 481 KB

Given {P n } n≥0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e., Necessary and sufficient conditions are given for the orthogonality of the sequence {Q n } n≥0 . An interesting interpretation in terms of the Jacobi