The function F(x)= (1/2 - x)(1 - x2)1/2 + x(1 + (1 - (1/2 + x)2)1/2) has a maximum of y=0.674981 at x=0.3437715 (Figure 1). This y value was found [1] to be a root of an irreducible polynomial over the integers of degree 10. The object of problem #7 is ...
Let (p"n)"n be a sequence of orthogonal polynomials with respect to the measure @m. Let T be a linear operator acting in the linear space of polynomials P and satisfying deg(T(p))=deg(p)-1, for all polynomial p. We then construct a sequence of ...
The authors first present a class of expansions in a series of Bernoulli polyomials and then show how this general result can be applied to yield various (known or new) polynomial expansions. The corresponding expansion problem involving the Euler ...
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