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The concept of special functions plays an important role in mathematical analysis and physics as well. In this paper, we study some different types of the special Gamma function defined on the two-fold fuzzy complex field, where we combine the classical Gamma function with the two-fold fuzzy algebra defined on complex numbers. On the other hand, many elementary properties of this new special function will be determined in terms of theorems and proofs. [ABSTRACT FROM AUTHOR]

Symbolic 3-plithogenic sets as a generalization of classical concept of sets were applicable to algebraic structures. The symbolic 3-plithogenic rings and fields are good generalizations of classical corresponding systems. In this paper, we study the symbolic 3-plithogenic real functions with one variable by using a special algebraic function called AH-isometry. In addition, we discuss the symbolic 3-plithogenic simple differential equations and conic sections by using this isometry. Also, many examples will be presented to explain the novelty of this work. [ABSTRACT FROM AUTHOR]

Symbolic 2-plithogenic sets as a generalization of classical concept of sets were applicable to algebraic structures. The symbolic 2-plithogenic rings and fields are good generalizations of classical corresponding systems. In this paper, we study the symbolic 2-plithogenic real functions with one variable by using a special algebraic function called AH-isometry. In addition, we discuss the symbolic 2-plithogenic simple differential equations and conic sections by using this isometry. Also, many examples will be presented to explain the novelty of this work. [ABSTRACT FROM AUTHOR]

The concept of unity roots plays a central role in the theory of field extensions and polynomials roots' computing. The objective of this paper is to find the algebraic formula for computing the symbolic 2-plithogenic and 3-plithogenic complex roots of unity, where a general formula will be provided with many related examples up to the exponent 3. [ABSTRACT FROM AUTHOR]