Freedman, David; Passow, Eli Degenerate Bernstein polynomials. (English) Zbl 0534.41005 J. Approximation Theory 39, 89-92 (1983). For \(f\epsilon\) C[0,1], the n-th Bernstein polynomial \(B_ n(f;x)\) is a polynomial of exact degree n, although degeneracies can occur in some cases. For example, if f itself is a polynomial of degree m, then \(B_ n(f;x)\) is also of degree m for \(n\geq m\) (although not equal to f(x) except in the case \(m=1)\). The result can be verified from an alternate form of \(B_ n(f;x).\) In the present note, the authors study a class of functions which has a sequence of degenerate Bernstein polynomials. Moreover, a surprising result on an equality for certain of these polynomials is established. Reviewer: V.Singh Cited in 1 ReviewCited in 4 Documents MSC: 41A10 Approximation by polynomials Keywords:Bernstein polynomial; degeneracy PDFBibTeX XMLCite \textit{D. Freedman} and \textit{E. Passow}, J. Approx. Theory 39, 89--92 (1983; Zbl 0534.41005) Full Text: DOI References: [1] Lorentz, G. G., Bernstein Polynomials (1953), Univ. of Toronto Press: Univ. of Toronto Press Toronto · Zbl 0051.05001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.