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- W3216765715 abstract "We consider a three-dimensional associative noncommutative algebra Ã2 over the field C, which contains the algebra of bicomplex numbers B(C) as a subalgebra. In this paper we consider functions of the form Φ(ζ)=f1(ξ1, ξ2,ξ3)I1+ f2(ξ1, ξ2,ξ3)I2+ f3(ξ1, ξ2,ξ3)ρ of the variable ζ= ξ1I1+ ξ2I2+ ξ3ρ, where ξ1, ξ2, ξ3 are independent complex variables and f1, f2, f3 are holomorphic functions of three complex variables. We construct in an explicit form all functions defined by equalities dΦ =dζ·Φ´(ζ) or dΦ = Φ´(ζ) ·dζ. The obtained descriptions we apply to representation of the mentioned class of functions by series. Also we established integral representations of these functions." @default.
- W3216765715 created "2021-12-06" @default.
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- W3216765715 date "2022-03-31" @default.
- W3216765715 modified "2023-10-14" @default.
- W3216765715 title "Differentiable functions in a three-dimensional associative noncommutative algebra" @default.
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- W3216765715 doi "https://doi.org/10.31197/atnaa.912344" @default.
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