Special functions

Special functions are some mathematical functions used in mathematical analysis or physics. Most of them appear in higher education. Some experts are studying numerical methods for them.

Definition

In mathematics, most functions are defined as a solution of a differential equation. For example, the exponential function is the solution of the ordinary differential equation . Due to this relation, some mathematicians are studying the connection between ODEs and special functions.

Examples

• Gamma function, it is studied since Euler
• Orthogonal polynomials, these are polynomials with special properties.
• Matrix functions, these are studied in linear algebra and matrix analysis.
• Riemann zeta function, related to the distribution of prime numbers in the Riemann hypothesis.
• Gauss error function, a function often used in probability theory

For more examples, find textbooks named "special functions".