△_(h)-GOULD-HOPPER APPELL POLYNOMIALS  

作　　者：Mehmet Ali ÖZARSLAN Banu YILMAZ YASAR 

机构地区：[1]Department of Mathematics,Eastern Mediterranean University,Famagusta,North Cyprus via Mersin 10,Turkey

出　　处：《Acta Mathematica Scientia》2021年第4期1196-1222,共27页数学物理学报（B辑英文版）

摘　　要：In this paper,we introduce the △_(h)-Gould-Hopper Appell polynomials An(x,y;h)via h-Gould-Hopper polynomials G_(n)^(h)(x,y).These polynomials reduces to △_(h)-Appell polynomials in the case y=0,△-Appell polynomials in the case y=0 and h=2D-Appell polynomials in the case h→0,2D △-Appell polynomials in the case h=1 and Appell polynomials in the case h→0 and y=0.We obtain some well known main properties 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 △_(h)-Gould-Hopper Appell polynomials reduce to determinant 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 △_(h)-Appell polynomials,△-Appell polynomials;recurrence,shift operators,differential and integro-differential equation of 2D-Appell polynomials,recurrence,shift operators,integrodifference equation of 2D △-Appell polynomials,recurrence,shift operators,differential 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,degenerate Gould-Hopper Carlitz Euler polynomials,degenerate Gould-Hopper Genocchi polynomials,△_(h)-Gould-Hopper Boole polynomials and △_(h)-Gould-Hopper Bernoulli polynomials of the second kind.In particular cases of the degenerate Gould-Hopper Carlitz Bernoulli polynomials,degenerate Gould-Hopper Genocchi polynomials,△_(h)-Gould-Hopper Boole polynomials and △_(h)-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 equat

关 键 词：△_(h)-Appell polynomials DETERMINANT RECURRENCE difference equation 

分 类 号：O174.14[理学—数学]