In mathematics, a multivalued function (also known as a multiple-valued function) is a function that has two or more values in its range for at least...

real numbers must be modified in a multivalued context: (ez)w ≠ ezw, but rather (ez)w = e(z + 2niπ)w multivalued over integers n See failure of power...

In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse...

known as multivalued functions in some references, but herein and in many others references in mathematical analysis, a multivalued function is a set-valued...

to consider these functions as multivalued functions. If log ⁡ z {\displaystyle \log z} denotes one of the values of the multivalued logarithm (typically...

hyperbolic sine function is typically written as arsinh(x). The expressions like sin−1(x) can still be useful to distinguish the multivalued inverse from...

it is a multivalued function with singularity at zero. The graphs of Bessel functions look roughly like oscillating sine or cosine functions that decay...

}{2n\left({2n}\right)!!}}}{\frac {1}{x^{2n}}}} As functions of a complex variable, inverse hyperbolic functions are multivalued functions that are analytic, except at a...

analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued. A simple...

domain of an analytic function (mathematics) Multivalued function – Generalized mathematical function Densely defined operator – Function that is defined almost...

glued together. Examples of Riemann surfaces include graphs of multivalued functions like √z or log(z), e.g. the subset of pairs (z,w) ∈ C2 with w =...

is no need to restrict the domain if we allow the inverse to be a multivalued function. In relational algebra, a selection (sometimes called a restriction...

Vector fields are one kind of tensor field. Coordinate vector Curve Multivalued function Parametric surface Position vector Parametrization In fact, these...

the power i only the principal value is chosen. When treated as multivalued functions, both sides produce the same set of values, being { e 2 π n | n...

{\displaystyle \ln(z)} is a multivalued function. In order to make ln ⁡ ( z ) {\displaystyle \ln(z)} a proper, single-output function, we therefore need to...

considered, the argument is a multivalued function operating on the nonzero complex numbers. The principal value of this function is single-valued, typically...

trigonometric function is monotonic, one can define an inverse function, and this defines inverse trigonometric functions as multivalued functions. To define...

mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the...

Dirac delta function: useful to describe physical phenomena such as point charges. Multivalued function: one-to-many relation. Random function: Random element...

setting, am ⁡ ( u , m ) {\displaystyle \operatorname {am} (u,m)} is a multivalued function (in u {\displaystyle u} ) with infinitely many logarithmic branch...

the result and select the correct branch of the multivalued function Arctan(y/x). The atan2 function is useful in many applications involving Euclidean...

root are allowed to be taken inconsistently, it is, in general, a multivalued function. To find the arithmetic–geometric mean of a0 = 24 and g0 = 6, iterate...

kernel as a generalised function with a (in general) random rather than certain value. That is, it is a multivalued function where the values are not...

surjection Bijective numeration Bijective proof Category theory Multivalued function Hall 1959, p. 3 There are names associated to properties (1) and...

logarithm function. No single valued function on the complex plane can satisfy the normal rules for logarithms. However, a multivalued function can be defined...

unique complex number w satisfying erf w = z, so a true inverse function would be multivalued. However, for −1 < x < 1, there is a unique real number denoted...

of this is that the "inverse" of the complex exponential function is a multivalued function taking each nonzero complex number z to the set of all logarithms...

with no need to rewrite functions in the pipeline. A second situation where List shines is composing multivalued functions. For instance, the nth complex...

Binary relation 1:1 correspondence, an older name for a bijection Multivalued function Correspondence (algebraic geometry), between two algebraic varieties...

there exists some y ∈ X such that xRy. Such a relation is called a multivalued function. For example, the red and green relations in the diagram are total...