Abstract
The problem under consideration is that of approximating classes of smooth functions by algebraic-trigonometric polynomials of the form , where is an algebraic polynomial of degree and is a trigonometric polynomial of order . The precise order of approximation by such polynomials in the classes and an upper bound for similar approximations in the class with are found. The proof of these estimates uses mixed series in Legendre polynomials which the author has introduced and investigated previously.Bibliography: 13 titles.
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