Special functions

In mathematics, most functions are defined as a solution of a differential equation.^[1] For example, the exponential function ${\displaystyle \exp(x)}$ is the solution of the ordinary differential equation ${\displaystyle y^{\prime }=y}$ . Due to this relation, some mathematicians are studying the connection between ODEs and special functions.^[1][5]

• Gamma function, it is studied since Euler^[1][6][7]
• Orthogonal polynomials, these are polynomials with special properties.^[8][9][10]
• Matrix functions, these are studied in linear algebra and matrix analysis.^[11]

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

• National Institute of Standards and Technology, United States Department of Commerce. NIST Digital Library of Mathematical Functions. Archived from the original on December 13, 2018.
• Eric W. Weisstein, Special Function at MathWorld.
• Special functions at EqWorld: The World of Mathematical Equations
• Special functions and polynomials by Gerard 't Hooft and Stefan Nobbenhuis (April 8, 2013)
• Numerical Methods for Special Functions, by A. Gil, J. Segura, N.M. Temme (2007).
• R. Jagannathan, (P,Q)-Special Functions
• Specialfunctionswiki, a wiki about special functions