In this paper,we introduce mon-symbolic method to obtain the generating functions of the hybrid class of Hermite-associated Laguerre and its associated polynomials.We obtain the series definitions of these hybrid spec...In this paper,we introduce mon-symbolic method to obtain the generating functions of the hybrid class of Hermite-associated Laguerre and its associated polynomials.We obtain the series definitions of these hybrid special polynomials.Also,we derive the double lacunary generating functions of the Hermite-Laguerre polynomials and the Hermite-Laguerre-Wright polynomials.Further,we find multiplicative and derivative operators for the Hermite-Laguerre-Wright polynomials which helps to find the symbolic differential equation of the Hermite-Laguerre-Wright polynomials.Some concluding remarks are also given.展开更多
Let F, N、A and N2 denote the properties of being finite, nilpotent, abelian and nilpotent of classes at most 2, respectively. Firstly we consider the class of finitely generated FTV-groups. Wc show that the property ...Let F, N、A and N2 denote the properties of being finite, nilpotent, abelian and nilpotent of classes at most 2, respectively. Firstly we consider the class of finitely generated FTV-groups. Wc show that the property FC is closed under finite extensions, and extend this result to finitely generated NF-groups. Secondly we prove that a finitely generated NF-group G is in the class ((FC)F, oo) if and only if G is an FA-group. Finally we prove that a finitely genera ted ATF-group in the class ((FC)F,∞)^* is an FM-group. Moreover, G/Z2(G) is finite.展开更多
文摘In this paper,we introduce mon-symbolic method to obtain the generating functions of the hybrid class of Hermite-associated Laguerre and its associated polynomials.We obtain the series definitions of these hybrid special polynomials.Also,we derive the double lacunary generating functions of the Hermite-Laguerre polynomials and the Hermite-Laguerre-Wright polynomials.Further,we find multiplicative and derivative operators for the Hermite-Laguerre-Wright polynomials which helps to find the symbolic differential equation of the Hermite-Laguerre-Wright polynomials.Some concluding remarks are also given.
文摘Let F, N、A and N2 denote the properties of being finite, nilpotent, abelian and nilpotent of classes at most 2, respectively. Firstly we consider the class of finitely generated FTV-groups. Wc show that the property FC is closed under finite extensions, and extend this result to finitely generated NF-groups. Secondly we prove that a finitely generated NF-group G is in the class ((FC)F, oo) if and only if G is an FA-group. Finally we prove that a finitely genera ted ATF-group in the class ((FC)F,∞)^* is an FM-group. Moreover, G/Z2(G) is finite.
