Approximation properties of Fejér- and de la Valleé-Poussin-type means for partial sums of a special series in the system

This paper is concerned with series of the form where is an even -periodic function with finite values and , Series of this type appear as a particular case of more general special series in ultraspherical Jacobi polynomials, which were first introduced and studied by the author. Partial sums of the form are shown to have a number of important properties, which give them an advantage over trigonometric Fourier sums of the form . Approximation properties of Fejer- and de la Vallee-Poussin-type means for the partial sums are studied. Bibliography: 7 titles.