Erifunktsioonid

Erifunktsioonid, often translated as "special functions," is a term used in mathematics to refer to a class of well-known mathematical functions that have been given special names and have acquired properties that are used recurrently in mathematical research, physics, and other sciences. These functions are not elementary functions, meaning they cannot be expressed as a finite combination of basic arithmetic operations, exponentials, logarithms, and trigonometric functions.

The study of special functions has a long history, dating back to the 18th century with the development of the theory of differential equations. Many special functions arise as solutions to ordinary differential equations that are important in various areas of physics and engineering. Examples include Bessel functions, Legendre polynomials, and hypergeometric functions.

These functions are characterized by their rich mathematical properties, such as integral representations, series expansions, differential equations they satisfy, and recurrence relations. Their importance stems from their ability to model a wide range of phenomena, from wave propagation and heat conduction to quantum mechanics and probability theory. Consequently, they are fundamental tools in applied mathematics, physics, engineering, statistics, and computer science. Understanding and utilizing special functions is crucial for solving many complex problems in science and technology.