Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T00:52:41.340Z Has data issue: false hasContentIssue false
  • English
  • Français

A Method of Evaluating Certain Determinants

Published online by Cambridge University Press:  20 January 2009

J. L. Burchnall
J. L. Burchnall
Affiliation:
The University, Durham.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

1. Let [ast] (s, t=0, 1, … n) be a square matrix of order n+1 and determinant |ast| and suppose that by repeated “isolation” of the variables the corresponding bilinear form has been expressed as

where, for all r,

Then

Now (1) implies, and is implied by, the identities

Thus, from any known identity of the form (4), subject to the condition (2), we may at once infer, using (3). the value of the corresponding determinant |ars|.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 2 , November 1954 , pp. 100 - 104
Copyright
Copyright © Edinburgh Mathematical Society 1954

References

REFERENCES

1.Burchnall, J. L., “Some determinants with hypergeometric elements”, Quart. J. of Math. (Oxford) (2), 3(1952), 151–157.CrossRefGoogle Scholar
2.Burchnall, J. L., “An algebraic property of the classical polynomials”, Proc. London Math. Soc. (3), I (1951), 232–240.CrossRefGoogle Scholar
3.Geronimus, J., “On some persymmetric determinants formed by the polynomials of M. Appell” Journal London Math. Soc., 6 (1931), 55–59.CrossRefGoogle Scholar
4.Burchnall, J. L., “A note on the polynomials of Hermite”, Quart. J. of Math. (Oxford), 12 (1941), 9–11.CrossRefGoogle Scholar
5.Burchnall, J. L. and Chaundy, T. W., “Expansions of Appell's double hypergeometric functions”, Quart. J. of Math. (Oxford), 11 (1940), 249–270.CrossRefGoogle Scholar
6.Burchnall, J. L. and Chaundy, T. W., “Expansions of Appell's double hypergeometric functions, II”, Quart. J. of Math. (Oxford), 12 (1941), 112–128.CrossRefGoogle Scholar
7.Appell, P. and Kampé de Fériet, J., Fonctions hypergéoétriques et hypersphériques (Paris, 1926).Google Scholar