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Gauss-Lobatto quadrature formulae associated with symmetric weight functions are considered. The kernel of the remainder term for classes of analytic functions is investigated on elliptical contours. Sufficient conditions are found ensuring that the kernel attains its maximal absolute value at the intersection point of the contour with either the real or(More)
Nanocrystalline soft magnetic materials combine low magnetic losses with high permeability and high saturation induction. Those properties are useful for power electronics. The linear behaviour below saturation allows superposition of losses in the frequency domain. The losses of three toroidal Vitroperm 500 F cores are investigated under square voltage.
Let pm(x) = P (λ) m (x)/P (λ) m (1) be the m-th ultraspherical polynomial normalized by pm(1) = 1. We prove the inequality |x|p 2 n (x)−pn−1(x)pn+1(x) ≥ 0, x ∈ [−1, 1], for −1/2 < λ ≤ 1/2. Equality holds only for x = ±1 and, if n is even, for x = 0. Further partial results on an extension of this inequality to normalized Jacobi polynomials are given.
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