The theory of slice regular functions (originally Cullen-regular functions) was born at George
Mason University, in Virginia, where the first and third authors collaborated for a 2-month …

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions;
however, in many applications, functions of interest are real-valued and hence not analytic …

In recent years, much attention has been paid to the role of classical special functions of a
real or complex variable in mathematical physics, especially in boundary value problems …

In this paper we study in detail the theory of bicomplex holomorphy, in the context of the
several ways in which bicomplex numbers can be considered. In particular we will show …

Holomorphic function theory is an effective tool for solving linear elasticity problems in the
complex plane. The displacement and stress field are represented in terms of holomorphic …

In this paper recently studied orthogonal Appell bases of solid spherical monogenics in R^ 3
R 3 are used to construct a polynomial basis of solutions to the Lamé equation from linear …

In complex analysis, every harmonic function admits a decomposition as a sum of a
holomorphic and an antiholomorphic function. However, this fact does not hold for …

The aim of this paper is to introduce, in the framework of Clifford analysis, the notions of φ φ-
hyperdifferentiability and φ φ-hyperderivability for ψ ψ-hyperholomorphic functions where …

Additive decompositions of harmonic functions play an important role in function theory and
for the solution of partial differential equations. One of the best known results is the …

The quotient of the function difference over the variable increment is evaluated in 1+ n finite
dimensional imaginary scator algebra. A distinctive property of the scator product is that it is …