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A new basis for discrete analytic polynomials

Published online by Cambridge University Press:  09 April 2009

Doron Zeilberger
Affiliation:
Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel.
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Abstract

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A new basis for discrete analytic polynomials is presented for which the series converges absolutely to a discrete analytic function in the upper right quarter lattice whenever

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

Atadzanov, B. A. (1974), ‘Representation of analytic functions of a discrete complex variable by means of basis elements’, Metričeskie Voprosy Teor. Funkcii, Otobražaniu 5, 1320 (Russian).Google Scholar
Boas, R. P. Jr, (1954), Entire Functions (Academic Press, New York).Google Scholar
Duffin, R. J. (1956), ‘Basic properties of discrete analytic functions’, Duke Math. J. 23, 335363.CrossRefGoogle Scholar
Duffin, R. J. and Elmore, L. Peterson (1968), ‘The discrete analogue of a class of entire functions’, J. Math. Anal. Appl. 21, 619642.CrossRefGoogle Scholar
Ferrand, J. (1944), ‘Fonctions préharmonique et fonctions préholomorphes’, Bull. Sci. Math. 68, 152180.Google Scholar
Rudin, W. (1966), Real and Complex Analysis (McGraw-Hill, New York).Google Scholar
Zeilberger, D. (to appear), ‘A new approach to the theory of discrete analytic functions’, J. Math. Anal. Appl.Google Scholar