Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-14T06:20:39.127Z Has data issue: false hasContentIssue false
  • English
  • Français

On a dual relation for addition formulas of additive groups, I

Published online by Cambridge University Press:  22 January 2016

Toshihiro Watanabe
Toshihiro Watanabe*
Affiliation:
Department of Applied Mathematics, Faculty of Engineering University of Gifu, Gifu, Japan
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.

This is the first in a series of papers concerned with a relation between a representation in the polynomial ring of additive groups and its translation invariant operators. The present study is to observe several properties of a polynomial sequence pa(x) satisfying the binomial identity:

by means of some translation invariant operators.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 94 , June 1984, pp. 171 - 191
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

[ 1 ] Abel, N. H., Démonstration d’une expression de laquelle la formule binome est un cas particulier, Oeuvres, 102–103, Johnson Reprint Cop., New York, (1973).Google Scholar
[ 2 ] Bell, E. T., The history of Blissard symbolic method with a sketch of the inventor’s life, Amer. Math. Monthly, 45, (1938), 414–421.Google Scholar
[ 3 ] Comtet, L., “Advanced Combinatorics”, Reidel, Dordrecht and Boston, 1974.Google Scholar
[ 4 ] Gould, H. D., Final analysis of Vandermonde’s convolution, Amer. Math. Monthly, 64 (1957), 409–415.Google Scholar
[ 5 ] Gould, H. D., A new convolution formula and some orthogonal relation for inversion of series, Duke Math. J., 29 (1962), 393–404.Google Scholar
[ 6 ] Mohanty, G., “Lattice Path Counting” and Application” Academic Press, New York, 1979.Google Scholar
[ 7 ] Pincherle, S., “Le Operazioni Distributive e le loro Applicazioni all’ Analisi”, Bologana, Zanichelli, 1901.Google Scholar
[ 8 ] Riorden, J., “Combinatorial Identities”, Robert E. Krieger Pub. Com., New York, 1979.Google Scholar
[ 9 ] Rota, G. C., Kahaner, D. and Odlyzko, A., Finite, operator calculas, J. Math. Anal. Appl., 42 (1973), 685–760.Google Scholar
[10] Takács, L., “Combinatorial Methods in the Theory of Stochastic Processes”, John Wiley & Sons, New York, London and Sydney, 1967.Google Scholar
[11] Szegö, G., “Orthogonal Polynomials”, Coll. Pub,, 23, Amer. Math. Soc, Providence, R. I. (1958).Google Scholar