The word "normal form" is used in a variety of different ways in mathematics. In general, it refers to a way of representing objects so that, although each may
have many different names, every possible name corresponds to exactly one object
(Petkovšek *et al. *1996, p. 7). For example, the term "normal
form" is used in linear algebra to describe matrices that have been transformed
into certain special forms (e.g., Hermite normal
form and Smith normal form), in logic to
describe statements formulated in a standard way involving so-called literals
(e.g., conjunctive normal form and disjunctive
normal form), and in the theory of special functions to mean the uniquely-determined
holonomic function (i.e., solution of a linear
homogeneous ordinary differential equation with polynomial coefficients) of lowest
order up to multiplication by polynomials (Koepf 1998, p. 2).

# Normal Form

## See also

Canonical Form, Conjunctive Normal Form, Disjunctive Normal Form, Hermite Normal Form, Holonomic Function, Literal, Normal-Form Game, Prenex Normal Form, Smith Normal Form## Explore with Wolfram|Alpha

## References

Koepf, W.*Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities.*Braunschweig, Germany: Vieweg, 1998.Petkovšek, M.; Wilf, H. S.; and Zeilberger, D.

*A=B.*Wellesley, MA: A K Peters, 1996. http://www.cis.upenn.edu/~wilf/AeqB.html.

## Referenced on Wolfram|Alpha

Normal Form## Cite this as:

Weisstein, Eric W. "Normal Form." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/NormalForm.html