【摘 要】
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In this paper,we introduce the Δh-Gould-Hopper Appell polynomials An(x,y;h)via h-Gould-Hopper polynomials Ghn(x,y).These polynomials reduces to Δh-Appell poly-nomials in the case y =0,Δ-Appell polynomials in the case y =0 and h =1,2D-Appell polynomials in
【机 构】
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Department of Mathematics,Eastern Mediterranean University,Famagusta,North Cyprus via Mersin 10,Turk
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In this paper,we introduce the Δh-Gould-Hopper Appell polynomials An(x,y;h)via h-Gould-Hopper polynomials Ghn(x,y).These polynomials reduces to Δh-Appell poly-nomials in the case y =0,Δ-Appell polynomials in the case y =0 and h =1,2D-Appell polynomials in the case h → 0,2D Δ-Appell polynomials in the case h =1 and Appell polynomials in the case h → 0 and y =0.We obtain some well known main proper-ties and an explicit form,determinant representation,recurrence relation,shift operators,difference equation,integro-difference equation and partial difference equation satisfied by them.Determinants satisfied by Δh-Gould-Hopper Appell polynomials reduce to determi-nant of all subclass of the usual polynomials.Recurrence,shift operators and difference equation satisfied by these polynomials reduce to recurrence,shift operators and difference equation of Δh-Appell polynomials,Δ-Appell polynomials;recurrence,shift operators,differ-ential and integro-differential equation of 2D-Appell polynomials,recurrence,shift operators,integro-difference equation of 2D Δ-Appell polynomials,recurrence,shift operators,differ-ential equation of Appell polynomials in the corresponding cases.In the special cases of the determining functions,we present the explicit forms,determinants,recurrences,difference equations satisfied by the degenerate Gould-Hopper Carlitz Bernoulli polynomials,degener-ate Gould-Hopper Carlitz Euler polynomials,degenerate Gould-Hopper Genocchi polynomi-als,Δh-Gould-Hopper Boole polynomials and Δh-Gould-Hopper Bernoulli polynomials of the second kind.In particular cases of the degenerate Gould-Hopper Carlitz Bernoulli polynomi-als,degenerate Gould-Hopper Genocchi polynomials,Δh-Gould-Hopper Boole polynomials and Δh-Gould-Hopper Bernoulli polynomials of the second kind,corresponding determinants,recurrences,shift operators and difference equations reduce to all subclass of degenerate so-called families except for Genocchi polynomials recurrence,shift operators,and differential equation.Degenerate Gould-Hopper Carlitz Euler polynomials do not satisfy the recurrences and differential equations of 2D-Euler and Euler polynomials.
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