In mathematics, a multivalued function, multiple-valued function, many-valued function, or multifunction, is a function that has two or more values in...

distinguish multivalued functions from set-valued functions (which they called set-valued relations) by the fact that multivalued functions only take multiple...

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

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...

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

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...

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...

Half-exponential function, a compositional square root of an exponential function Lambert W function#Solving equations – Multivalued function in mathematics...

article. The Bessel function of the first kind is an entire function if α is an integer, otherwise it is a multivalued function with singularity at zero...

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

has a unique cube root, which is zero itself. The cube root is a multivalued function. The principal cube root is its principal value, that is a unique...

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

field of complex analysis, a branch point of a multivalued function is a point such that if the function is n {\displaystyle n} -valued (has n {\displaystyle...

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

}{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 finite...

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

inverse functions are proper (i.e. strict) subsets of the domains of the original functions. For example, using function in the sense of multivalued functions...

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...

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

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

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

{\displaystyle \circ } takes two functions, f {\displaystyle f} and g {\displaystyle g} , and returns a new function h ( x ) := ( g ∘ f ) ( x ) = g (...

{\displaystyle \sin(2\pi )=0} , and so on. It follows that the arcsine function is multivalued: arcsin ⁡ ( 0 ) = 0 {\displaystyle \arcsin(0)=0} , but also arcsin...

In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle...

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

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...

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

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

complex number x can thus be taken to be a multivalued function. By convention the principal value of this function, called the principal root and 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...