Primitive transcendental functions and symbolic computation

This paper presents the theoretical support for a novel and efficient approach to represent and deal symbolically with an important ensemble of complex functions. These functions are characterized by a Maclaurin series expansion whose general term may be factoring as: b(j)T(j+k) x(j)/j(!) where b(j) is periodic, k is an element of Z and {T-m} is a complex sequence that characterizes a family of functions. The functions are structured in families of Euclidean vector spaces that facilitate a discrete vector representation. The used representations provide important facilitates for the symbolic computation of divers operators/operations that are executed by the computation of their "dual counterparts" into the representation space. (C) 2017 Elsevier Ltd. All rights reserved.