In mathematics, several functions are important enough to deserve their own name. This is a listing of pointers to those articles which explain these functions in more detail.

Table of contents |

2 Special functions 3 Number theoretic functions 4 Other |

## Elementary functions

- Polynomials: can be generated by addition and multiplication alone.
- Square root: yields a number whose square is the given one.
- Exponential function: raise a fixed number to a variable power.
- Logarithm: the inverses of exponential functions; useful to solve equations involving exponentials.
- Trigonometric functions: sine, cosine, etc.; used in geometry and to describe periodic phenomena.
- Hyperbolic functions: formally similar to the trigonometric functions.
- Absolute value: drops the sign of a given number.
- Floor function: largest integer ≤ a given number.

## Special functions

- Gamma function: A generalization of the factorial function.
- Riemann zeta function: A special case of Dirichlet series.
- Elliptic integrals: Arising from the path length of ellipses; important in many applications.
- Elliptic functions: The inverses of elliptic integrals; used to model double-periodic phenomena.
- Bessel functions: Defined by a differential equation; useful in astronomy, electromagnetism, and mechanics.
- Logarithmic integral: Integral of the reciprocal of the logarithm, important in the prime number theorem.
- Lambert's W function: inverse of
*f*(*w*) =*w*exp(*w*). - Error function: an integral important for normal random variables.

## Number theoretic functions

- sigma function: Sums of powers of factors of a given natural number.
- Euler's phi function: Number of numbers relatively prime to a given one.
- Prime counting function: Number of primess less than or equal to a given number.
- Partition function: Order-independent count of ways to write a given positive integer as a sum of positive integers.

## Other

- Ackermann function: in the theory of computation, a recursive function that is not primitive recursive.
- Dirac delta function: everywhere zero except for
*x*= 0; total integral is 1. Not a function but a distribution. - Heaviside step function: 0 for negative arguments and 1 for positive arguments. The integral of the Dirac delta distribution.