An elementary number is one formalization of the concept of a
closed-form number. The elementary numbers form an
algebraically closed field containing the roots of arbitrary expressions using
field operations,
exponentiation, and
logarithms. The set of the elementary numbers is subdivided into the explicit elementary numbers and the implicit elementary numbers.
References
Ritt, Joseph Fels (1948). Integration in finite terms. Liouville's theory of elementary methods. New York: Columbia University press. p. 60.