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Paper details
Number 4 - December 1997
Volume 7 - 1997
On 2-D polynomials and discrete-continuous systems
Zdzisław W. Trzaska
Abstract
The paper deals with 2-D polynomials Q(x, y) and R(x, y) having real coefficients, which are generated by modified first and second numerical triangles (FMNT) and (SMNT), respectively. It has been proven that n-th-degree polynomials Qn(X, y) and Rn(x, y) can be easily determined as solutions of third order recurrences with coefficients depending on x and y with appropriate initial conditions. Suitable expressions are involved and simple formulae are established to check links between Q(x, y) and R(x, y) . Problems connected to the efficiency of the 2-D polynomials in solutions to practical problems are also considered. Examples illustrating possible applications of the presented approach are also demonstrated.
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