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List of mathematical functions
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List of functions
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
1 Elementary functions
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
primes
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.
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