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Differentiability of pseudo-dual-quaternionic functions with a differential operator. (English) Zbl 1438.32017

Summary: This paper introduces the new concept of pseudo-dual-quaternions and some of their basic properties based on matrices. We extend the concept of differentiability to pseudo-dual-quaternionic functions. Also, we propose a corresponding Cauchy-Riemann formulas induced the properties of a holomorphic function of pseudo-dual-quaternionic variables.

MSC:

32A99 Holomorphic functions of several complex variables
32W50 Other partial differential equations of complex analysis in several variables
30G35 Functions of hypercomplex variables and generalized variables
11E88 Quadratic spaces; Clifford algebras
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