Means, generalized divided differences, and intersections of osculating hyperplanes
The author offers a new mean value theorem for functional determinants of extended complete Chebyshev systems [as defined in \textit{S. Karlin} and \textit{W. J. Studden}; ``Tchebycheff systems: With applications in analysis and statistics'' (1966; Zbl 0153.38902), except that there the functional determinants were supposed to be positive, while here only to be nonzero] and, based on this, a result stating essentially that under certain assumptions the \(n\) osculating hyperplanes at a point in the \(n\)-dimensional real space intersect in a single point. This defines \(n\) mean values which generalize several known ones (arithmetic, geometric, harmonic, logarithmic, etc.).
scientific article; zbMATH DE number 894223