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...

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

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...

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

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...

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...

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...

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

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...

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

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...

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...

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...

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

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

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...

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...

Mathematical correspondence, a more general term than bijection Multivalued function Correspondence (algebraic geometry), between two algebraic varieties...

also on the path along which the integral is taken; it is thus a multivalued function of z {\displaystyle z} . Abelian integrals are natural generalizations...

be multivalued. Additionally, certain classes of functions may be obtained by others using the final two rules. For example, the exponential function e...

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

(real) natural logarithm. As arg is a multivalued function, unique only up to a multiple of 2π, log is also multivalued. The principal value of log is often...