Abstract
For the infinite triangular arrays of points whose rows consist of (i) the nth roots of unity, (ii) the extrema of Chebyshev polynomials Tn(x) on [—1,1], and (iii) the zeros of Tn(x), we consider the corresponding sequences of divided difference functionals {In}f in the successive rows of these arrays. We investigate the totality of such functionals as well as the convergence of the generalized Taylor series Li°(A»/)^n-i( z ) f° r a function/, where the Pk are basic polynomials satisfying lH1Pk = Sjlc. Explicit formulae are given for the basic polynomials involving the Mobius function (of number theory), and examples of non-trivial functions/for which /„/ = 0, n = 1,2,..., are constructed.
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