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On approximation of XN by incomplete polynomials

✍ Scribed by I Borosh; C.K Chui; P.W Smith

Publisher: Elsevier Science
Year: 1978
Tongue: English
Weight: 370 KB
Volume: 24
Category: Article
ISSN: 0021-9045
DOI: 10.1016/0021-9045(78)90027-8

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By establishing an identity for \(S_{n}(x):=\sum_{j=0}^{n}|j / n-x|\left({ }_{j}^{n}\right) x^{j}(1-x)^{n-j}\), the present paper shows that a pointwise asymptotic estimate cannot hold for \(S_{n}(x)\), and, at the same time, obtains a better result than that in Bojanic and Cheng [3]. 1993 Academic