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We generate, from a given basic set of polynomials in several complex variables , new basic sets of polynomials and generated by the application of the Δ and ∇  operators to the set . All relevant properties relating to the effectiveness in Reinhardt and hyperelliptic domains of these new sets are properly deduced. The case of classical orthogonal polynomials is investigated in details and the results are given in a table. Notations are also provided at the end of a table.

journal of applied mathematics and physics

Forward (&amp;#916) and Backward (&amp;#8711) Difference Operators Basic Sets of Polynomials in &lt;img src=&quot;http://file.scirp.org/html/70175_c1.jpg&quot; width=&quot;20&quot;&gt; and Their Effectiveness in Reinhardt and Hyperelliptic Domains