Persymmetric Research Articles

XXIII.—On some Persymmetric Determinants

We consider in this paper the persymmetric determinantswherep(x) being a function which is not negative in the interval (a, b) (finite or infinite); we suppose further that the integralsexist fors= 0, 1, 2,….The object of this paper is the application of a theorem stated by the writer in the paper “Sur un déterminant de Hankel” to many determinants of the type (1), referred to by Sir Thomas Muir in his paper “The theory of persymmetric determinants from 1894 to 1919.”

On Some Persymmetric Determinants formed by the Polynomials of M. Appell

Journal of the London Mathematical SocietyVolume s1-6, Issue 1 p. 55-59 Notes and Papers On Some Persymmetric Determinants formed by the Polynomials of M. Appell Correction(s) for this article Corrigenda: A Sufficiency Condition for Poisson's Formula* E. H. Linfoot, Volume s1-6Issue 1Journal of the London Mathematical Society pages: 80-80 First Published online: December 23, 2016 J. Geronimus, J. GeronimusSearch for more papers by this author J. Geronimus, J. GeronimusSearch for more papers by this author First published: January 1931 https://doi.org/10.1112/jlms/s1-6.1.55Citations: 7AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volumes1-6, Issue1January 1931Pages 55-59 RelatedInformation

Persymmetric Determinants whose Elements are the Integrals of Legendre's Polynomials

In a paper on ' Determinants involving specified numbers,' three persymmetric determinants whose elements are integrals of Legendre's Polynomials were taken and their values given without proof.† In this paper, the missing proof and a general mode of evaluation are supplied along with a few more new results.

II.—The Theory of Persymmetric Determinants from 1894 to 1919

The twenty-year period, 1900–1920, shows a marked increase in the number of writings concerned with persymmetric determinants. There is, it is true, a still greater rate of increase of those of them that belong to the class of “solved questions,” but even taking this into account, we find a growth of interest in the subject that is distinctly striking. And then, too, we must guard carefully against accepting the belief that the members of this solved-question class are uniformly of slight importance, and that the others are never trivial.

Aggregates of minors of persymmetric determinants

Aggregates of minors of persymmetric determinants

XXV.—The Theory of Persymmetric Determinants in the Historical Order of Development up to 1860

As has already been pointed out (Hist., i. pp. 485–487), the special form of determinant named “persymmetric” in 1853 by Sylvester came first to light in 1835 in a paper of Jacobi's on the elimination of the unknown from two equations of the nth degree, the fact being that the adjugate of Bezout's condensed eliminant—in other words, the adjugate of the determinant resulting from Bezout's “abridged method“ of elimination—is there shown to be such that the elements of it whose place-numbers have the same sum are equal.

Vanishing Aggregates of Determinant Minors

1. Since a persymmetric determinant is a particular case of an axisymmetric determinant, it follows that every type of vanishing aggregate for axisymmetric determinants is also a vanishing aggregate for persymmetric determinants. The principal object of this paper is to give a series of theorems (I., II., III., IV., V.), by the application of which to any vanishing aggregate of minors of persymmetric determinants new vanishing aggregates are obtained (7–12), which, though true for persymmetric, are no longer true for axisymmetric determinants.