Special functions facts for kids
Special functions are special kinds of mathematical tools. They are used a lot in advanced math and physics. Think of them as super useful formulas that help scientists and engineers solve complex problems. Experts also study how to use computers to work with these functions.
What Are Special Functions?
In mathematics, many functions are defined by how they change. This change is described by something called a differential equation. Imagine you have a rule that tells you how fast something grows or shrinks. A differential equation is like that rule.
For example, the exponential function (written as 
) is a special function. It's defined by a simple rule: its rate of change is always equal to its current value. Mathematicians study how these special functions are connected to these change rules.
Examples of Special Functions
There are many different types of special functions. Here are a few examples:
- Gamma function: This function is like a super-version of the factorial (like 5! = 5x4x3x2x1). It was first studied by a famous mathematician named Leonhard Euler.
- Orthogonal polynomials: These are special kinds of polynomials (math expressions with variables and numbers). They have unique properties that make them very useful in areas like signal processing and quantum mechanics.
- Matrix functions: These functions work with matrices, which are like grids of numbers. They are used in linear algebra, a branch of math that deals with vectors and matrices.
If you want to learn more, you can find many textbooks about "special functions."
See also
In Spanish: Función especial para niños
External Links
- 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.
