erikoisfunktio

Erikoisfunktio is a term of Finnish origin that translates to "special function" in English. In mathematics, special functions are a class of mathematical functions that have established names and associated properties, often arising in the solutions of differential equations or in areas like calculus, physics, and engineering. These functions are typically considered "special" because they are not elementary functions, such as polynomials, exponentials, logarithms, or trigonometric functions, which can be expressed using a finite number of basic operations.

The study of special functions is a significant branch of mathematics. Many of these functions, like the Gamma function, Bessel functions, Legendre polynomials, and the Riemann zeta function, have broad applicability. They appear when solving problems involving wave propagation, heat conduction, quantum mechanics, and number theory, among other fields. Their importance stems from their ability to describe complex phenomena concisely and to provide standardized tools for analysis. The definition, properties, and relationships between these functions are extensively studied and documented in mathematical literature.