Special functions

nonnegative number with the same magnitude as a given real number

mathematical function that extracts the sign of a real number or complex number

discontinuous function whose value is zero for negative numbers and one for positive numbers

probability distribution

function that can be defined as the root of a polynomial equation

functions of a real returning respectively the largest smaller and the smallest larger integer

analytic function that does not satisfy a polynomial equation

mathematical function

functions which have established names and notations due to their importance in mathematics

total non-primitive-recursive computable function

special function defined by an integral

complex-valued function that is holomorphic at all finite points over the whole complex plane

term in mathematics

multivalued function that is the inverse of the map z ↦ z exp(z)

analytic function on the upper half-plane with a certain behavior under the modular group

real function of real variable that is piecewise constant with a finite number of regions

function whose graph is 0, then 1, then 0 again, in an almost-everywhere continuous way

mathematical formula built with arithmetic operations and other previously defined functions

special function defined by an integral

polynomial sequence

continuous function that is not absolutely continuous

In mathematics, the polylogarithm (also known as '''Jonquière's function, for Alfred Jonquière) is a special function of order and argument . Only for special values of does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function. In quantum statistics, the polylogarithm function appears as the closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the Bose–Einstein integral'''. In quantum electrodynamics, polylogarithms of positive integer order arise in the c

function that is discontinuous at rationals and continuous at irrationals

special function defined by an integral

mathematical function

special function in the physical sciences

tent function, often used in signal processing

thumbnail|upright=1.3|Plot of logit(x) in the domain of 0 to 1, where the base of the logarithm is e.

periodic distribution ("function") of "point-mass" Dirac delta sampling

piecewise function that clamps its input to be non-negative

improper integral of sin(𝑥)∕𝑥 from 0 to ∞

entire function depending on two complex parameters α and β

mathmatical function

mathematical function

probability distribution often used in spectroscopy and diffraction

thumb|right|325px|The dilogarithm along the real axis thumb|right|325px|The principal value of the dilogarithm plotted in the complex plane

solutions to Mathieu's differential equations, which are second order linear differential equation

REDIRECT Logarithm#cologarithm

special function

concept in mathematics

mathematical function related to the gamma function

fractal-like continuous function that maps quadratic irrationals to rationals, and rationals to dyadic rationals

in mathematics, named after Gabriel Sudan

inequality of Jacobi polynomials

online project meant to be a collection of special functions

Special functions in mathematics

physics function introduced by Eugen von Lommel

mathematical reference work edited by M. Abramowitz and I. Stegun

mathematical function

expansion of exponentials of trigonometric functions in the basis of their harmonics

mathematical function

mathematic term

counterexample to the converse of the intermediate value theorem

mathematical integral

concept in mathematics

mathematical function

type of mathematical function

solutions of Lamé's equation