ABSTRACT. This paper describes the analogs of the Appell polynomial families in the context of algebras with two states, also called the c-free probability theory, introduced by Bożejko, Speicher, and Leinert. This theory includes as two extreme cases the free and Boolean probability theories. We prove recursions, generating functions, and factorization and martingale properties for these polyn...

In this paper, the effect of normal impact on the mathematical modeling of flexible multiple links is investigated. The response of such a system can be fully determined by two distinct solution procedures. Highly nonlinear differential equations are exploited to model the falling phase of the system prior to normal impact; and algebraic equations are used to model the normal collision of this ...

Mathematicians often speak of the unity of their subject. Such a unity from the 19th century origins in the history of linear ordinary differential equations, especially those closely connected with elliptic and modular functions. It is concerned with the impact of group theoretical and geometrical ideas upon the problem of understanding the nature of the solutions to a differential equation (s...

The focus of the research presented in this paper is on a new generalized family degenerate three-variable Hermite–Appell polynomials defined here using fractional derivative. was motivated by investigations Hermite-based Appell introduced R. Alyosuf. We show that, for certain values, well-known polynomials, and are seen as particular cases family. As results investigation, operational rule exp...

Recently, several Bell based polynomials such as Bernoulli, Euler, Genocchi and Apostol versions were defined investigated. The main aim of this paper is to introduce the general family Appell polynomials, which includes many new members in addition existing ones, investigate their properties including determinantal representation, recurrence relation, derivative formula, shift operators differ...