Geodesic
Moment Sequences and the Bernstein Polynomials*
Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 401-411

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The Bernstein polynomials (1.1) and the Bernstein power series (1.2) have been the subject of much research (e. g. [1; 2; 3; 6; 7; 8]). It is the purpose of this paper to demonstrate the relationship between these linear operators and certain classes of moment sequences defined below. 
Eisenberg, Sheldon M. Moment Sequences and the Bernstein Polynomials*. Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 401-411. doi: 10.4153/CMB-1969-050-8
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     author = {Eisenberg, Sheldon M.},
     title = {Moment {Sequences} and the {Bernstein} {Polynomials*}},
     journal = {Canadian mathematical bulletin},
     pages = {401--411},
     year = {1969},
     volume = {12},
     number = {4},
     doi = {10.4153/CMB-1969-050-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-050-8/}
}
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