Eielementaarisia

"Eielementaarisia" is the Finnish partitive plural form of the adjective "eielementaarinen", literally "not elementary" or "non-elementary". The word is formed from the negation "ei" and "elementaarinen" (elementary) and is used to describe objects, problems or properties that do not fall within a simple, elementary class or cannot be constructed by elementary means.

In mathematics and analysis the term commonly refers to functions or expressions that cannot be expressed by a finite combination of elementary functions (polynomials, exponentials, logarithms, trigonometric functions and their inverses). Examples of such non-elementary functions include many special functions such as the gamma function, error function and Bessel functions, which are typically defined by integrals, series or differential equations rather than elementary algebraic operations.

In logic and theoretical computer science "non-elementary" (eielementaarisia in Finnish contexts) describes decision problems or complexity bounds that grow faster than any fixed finite tower of exponentials. Notable examples include certain logical decision procedures and the Ackermann-type growth rates that exceed elementary recursive bounds.

Outside technical fields, the adjective may be used more loosely in Finnish to denote something that is complex, advanced or not basic. The closest English equivalent is "non-elementary" or "not elementary", with domain-specific meanings in mathematics and complexity theory.