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III.—On some Problems involving the Persymmetric Determinants*

Published online by Cambridge University Press:  15 September 2014

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Extract

Consider a system of “orthogonal polynomials”

P0, P1 (x), P2(x), …

possessing the property

x1, x2, …, xr being real given numbers, and p (x) a given “weight” function.

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Proceedings
Copyright
Copyright © Royal Society of Edinburgh 1932

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References

page 15 note * Appell, P., “Sur une classe de polynomes,” Annales de l'École Normale, t. 9 (1880), pp. 119144.CrossRefGoogle Scholar

page 16 note * Jacobi, C., “Ueber die Darstellung einer Reihe gegebener Werthe durch eine gebrochene rationale Funktion.”—Gesammelte Werke, t. iii, SS. 479511.Google Scholar

page 17 note Brioschi, F., “Intorno ad alcune questioni d'algebra superiore,” Opere Matematiche, t. i, pp. 127142.Google Scholar

page 17 note † Sylvester, J., “On a remarkable discovery in the theory of canonical forms and of hyperdeterminants,” Collected Mathematical Papers, t. i, pp. 265283.Google Scholar

page 18 note * Geronimus, J., “Sur un problème d'Hermite,” Bulletin de la Classe des Sciences Physiques et Mathématiques de l'Académie des Sciences d'Ukraine, t. iv, fasc. 5 (1930), pp. 295298.Google Scholar