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This article is about multivalued functions as they are considered in mathematical analysis. For set-valued functions as considered in variational analysis, see set-valued function.
Not to be confused with Multivariate function.
Multivalued function {1,2,3} → {a,b,c,d}.
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 one point in its domain.[1] It is a set-valued function with additional properties depending on context. The terms multifunction and many-valued function are sometimes also used.
A multivalued function of sets f : X → Y is a subset
Write f(x) for the set of those y ∈ Y with (x,y) ∈ Γf. If f is an ordinary function, it is a multivalued function by taking its graph
They are called single-valued functions to distinguish them.
^"Multivalued Function". Wolfram MathWorld. Retrieved 10 February 2024.
and 23 Related for: Multivalued function information
In mathematics, a multivaluedfunction (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...
to consider these functions as multivaluedfunctions. If log z {\displaystyle \log z} denotes one of the values of the multivalued logarithm (typically...
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivaluedfunction, 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...
it is a multivaluedfunction 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 multivaluedfunctions that are analytic, except at a...
analysis, the principal values of a multivaluedfunction are the values along one chosen branch of that function, so that it is single-valued. A simple...
the power i only the principal value is chosen. When treated as multivaluedfunctions, both sides produce the same set of values, being { e 2 π n | n...
setting, am ( u , m ) {\displaystyle \operatorname {am} (u,m)} is a multivaluedfunction (in u {\displaystyle u} ) with infinitely many logarithmic branch...
domain of an analytic function (mathematics) Multivaluedfunction – Generalized mathematical function Densely defined operator – Function that is defined almost...
{\displaystyle \ln(z)} is a multivaluedfunction. In order to make ln ( z ) {\displaystyle \ln(z)} a proper, single-output function, we therefore need to...
Dirac delta function: useful to describe physical phenomena such as point charges. Multivaluedfunction: one-to-many relation. Random function: Random element...
applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers R {\displaystyle \mathbb...
trigonometric function is monotonic, one can define an inverse function, and this defines inverse trigonometric functions as multivaluedfunctions. To define...
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...
logarithm function. No single valued function on the complex plane can satisfy the normal rules for logarithms. However, a multivaluedfunction can be defined...
kernel as a generalised function with a (in general) random rather than certain value. That is, it is a multivaluedfunction where the values are not...
the result and select the correct branch of the multivaluedfunction Arctan(y/x). The atan2 function is useful in many applications involving Euclidean...
of this is that the "inverse" of the complex exponential function is a multivaluedfunction taking each nonzero complex number z to the set of all logarithms...
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...
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