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Regularity and explicit representation of (0,1,...,m−2,m) interpolation on the zeros of (1−x2)Pn−2/(α,β)(x)

✍ Scribed by Yingguang Shi

Publisher
Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
1995
Tongue
English
Weight
714 KB
Volume
11
Category
Article
ISSN
0168-9673

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A necessary and sufficient condition of regularity of \((0,1, \ldots, m-2, m)\)-interpolation on the zeros of the Jacobi polynomials \(P_{n}^{(x, \beta)}(x)(\alpha, \beta \geqslant-1)\) in a manageable form is established. Meanwhile, the explicit representation of the fundamental polynomials, when t

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Regularity of (0, 1, ..., r − 2, r) and (0, 1, ..., r − 2, r)* Interpolations on Some Sets of the Unit Circle
✍ S.Q. Xie 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 149 KB

The purpose of this paper is to show regularity of \((0,1, \ldots, r-2, r)\) and \((0,1, \ldots, r-2, r)^{*}\) interpolations on the sets obtained by projecting vertically the zeros of \(\left.\left(1-x^{2}\right) P_{n}^{(\alpha, \beta)}(x)(-1)<\alpha, \beta \leqslant \frac{1}{2}\right),(1-x) P_{n}^