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Type of mathematical function
In mathematics, a constant function is a function whose (output) value is the same for every input value. As a real-valued function of a real-valued argument
Constant_function
Linear combination of indicator functions of real intervals
intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. A function f : R → R {\displaystyle f\colon
Step_function
Type of mathematical function
In mathematics, a locally constant function is a function from a topological space into a set with the property that around every point of its domain
Locally_constant_function
Multiplicative factor in a mathematical expression
polynomial, and these may be non-constant functions. A coefficient is a constant coefficient when it is a constant function. For avoiding confusion, in this
Coefficient
Function or value which does not change
mathematical constant or physical constant are sometimes used to distinguish this meaning. A function whose value remains unchanged (i.e., a constant function).
Constant_(mathematics)
Base of natural logarithms
The number e is a mathematical constant that is the base of the natural logarithm and exponential function. It is approximately equal to 2
E_(mathematical_constant)
Linear map or polynomial function of degree one
a polynomial function of degree zero (a constant polynomial) or one (a linear polynomial). For distinguishing such a linear function from the other
Linear_function
Class of mathematical function
denominator not constant 0) defined on D {\displaystyle D} , where the poles are the zeros of the denominator. Intuitively, a meromorphic function is a ratio
Meromorphic_function
Difference between logarithm and harmonic series
x.\end{aligned}}} Here, ⌊·⌋ represents the floor function. The numerical value of Euler's constant, to 50 decimal places, is: 0.57721 56649 01532 86060
Euler's_constant
Constant expressing ambiguity from indefinite integrals
constant of integration, often denoted by C {\displaystyle C} (or c {\displaystyle c} ), is a constant term added to an antiderivative of a function f
Constant_of_integration
Rules for computing derivatives of functions
constant function is 0, because the tangent line to the constant function is horizontal and its angle is 0. In other words, the value of the constant
Differentiation_rules
List of physical constants Particular values of the Riemann zeta function Particular values of the gamma function Physical constant Both i and −i are
List of mathematical constants
List_of_mathematical_constants
Property of two varying quantities with a constant ratio
(or normalizing constant). Two sequences are inversely proportional if corresponding elements have a constant product. Two functions f(x) and g(x) are
Proportionality_(mathematics)
Type of market maker
Constant-function market makers (CFMM) are a paradigm in the design of trading venues where a trading function and a set of rules determine how liquidity
Constant function market maker
Constant_function_market_maker
Polynomial function of degree at most one
called the slope of the function and of the line (see below). If the slope is a = 0 {\displaystyle a=0} , this is a constant function f ( x ) = b {\displaystyle
Linear_function_(calculus)
Function returning minus 1, zero or plus 1
Heaviside step function Negative number Rectangular function Sigmoid function (Hard sigmoid) Step function (Piecewise constant function) Three-way comparison
Sign_function
Strong form of uniform continuity
called the Lipschitz constant of the function (and is related to the modulus of uniform continuity). For instance, every function that is defined on an
Lipschitz_continuity
Mathematical function, denoted exp(x) or e^x
exponent to which a constant number e ≈ 2.718, the base, is raised. There are several other definitions of the exponential function, which are all equivalent
Exponential_function
Characteristic time in a system
response, or using an input that is a simple sinusoidal function of time) the time constant also determines the bandwidth of a first-order time-invariant
Time_constant
Value that is not changed during execution
* someOtherFunction(myFloat); // ... } the expression that the constant is initialized to are not themselves constant. Use of constantness is not necessary
Constant (computer programming)
Constant_(computer_programming)
Function with a repeating pattern
known as the period. More formally, a function f {\displaystyle f} is periodic if there exists a nonzero constant P {\displaystyle P} such that f ( x +
Periodic_function
Smooth approximation of one-hot arg max
The softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution
Softmax_function
Ratio of polynomial functions
which is undefined. A constant function such as f(x) = π is a rational function since constants are polynomials. The function itself is rational, even
Rational_function
Order-preserving mathematical function
monotone need not be invertible; they may be constant on some interval (and therefore not one-to-one). A function may be strictly monotonic over a limited
Monotonic_function
Mathematical constant
Glaisher–Kinkelin constant or Glaisher's constant, typically denoted A, is a mathematical constant, related to special functions like the K-function and the Barnes
Glaisher–Kinkelin_constant
Instantaneous rate of change (mathematics)
deducing derivatives of many functions from the derivatives of the basic functions: Constant rule If f is a constant function, then for all x, f′(x)=0
Derivative
Function computable with bounded loops
number n {\displaystyle n} and every k {\displaystyle k} , the k-ary constant function, defined by C n k ( x 1 , … , x k ) = d e f n {\displaystyle C_{n}^{k}(x_{1}
Primitive_recursive_function
Spectral density of light emitted by a black body
}{k_{\mathrm {B} }T}}\right)-1}}} where kB is the Boltzmann constant, h is the Planck constant, and c is the speed of light in the medium, whether material
Planck's_law
Solution to x * e^x = 1
can be extended to other values of the W function (see also Lambert W function § Representations). The constant Ω is transcendental. This can be seen as
Omega_constant
"Smoothing" integral transform
Gaussian will have a total integral of 1, with the consequence that constant functions are not changed by the Weierstrass transform. Instead of F ( x ) {\displaystyle
Weierstrass_transform
Mathematical function
real-valued function with a connected domain, the image is either an interval or a single value. In the latter case, the function is a constant function. The
Function_of_a_real_variable
Physical constant in quantum mechanics
The Planck constant, or Planck's constant, denoted by h {\displaystyle h} , is a fundamental physical constant of foundational importance in quantum mechanics:
Planck_constant
Lattice in universal algebra
the empty conjunction, i.e., the constant 1), and the constant 0. V = [∨, 0, 1] is the set of disjunctive functions: f(a ∨ b) = f(a) ∨ f(b). Equivalently
Post's_lattice
Association of one output to each input
They include constant functions, linear functions and quadratic functions. Rational functions are quotients of two polynomial functions, and their domain
Function_(mathematics)
Mathematical construction
the other hand, germs of smooth functions can distinguish between the constant function with value one and the function 1 + e − 1 / x 2 {\displaystyle
Stalk_(sheaf)
Function defined by multiple sub-functions
correct sub-function—and produce the correct output value. A step function or piecewise constant function, composed of constant sub-functions Piecewise
Piecewise_function
Fixed number that has received a name
\infty }\left(1+{\frac {1}{n}}\right)^{n}} The constant e is intrinsically related to the exponential function x ↦ e x {\displaystyle x\mapsto e^{x}} . The
Mathematical_constant
Symbolic description of a mathematical object
define the function that associates to each number its square plus one. An expression with no variables would define a constant function. Usually, two
Expression_(mathematics)
Theorem about the range of an analytic function
the plane into the unit disc via a holomorphic function, which implies that f {\textstyle f} is constant by Liouville's theorem. This theorem is a significant
Picard_theorem
Symbol representing a mathematical object
of x define constant functions and are therefore called constant. For example, a constant of integration is an arbitrary constant function that is added
Variable_(mathematics)
Constant a such that af(x) is a probability measure
normalizing constant or normalizing factor is used to reduce any nonnegative function whose integral is finite to a probability density function. For example
Normalizing_constant
Mathematical theorem in complex analysis
{\displaystyle f} . In other words, either f {\displaystyle f} is locally a constant function, or, for any point z 0 {\displaystyle z_{0}} inside the domain of
Maximum_modulus_principle
Mathematical term
slope: m = 1 {\displaystyle m=1} A "horizontal" line (the graph of a constant function) has zero slope: m = 0 {\displaystyle m=0} . A "vertical" line has
Slope
Concept in economics
Constant elasticity of substitution (CES) is a common specification of many production functions and utility functions in neoclassical economics. CES holds
Constant elasticity of substitution
Constant_elasticity_of_substitution
Mathematical inequality in Sobolev space theory
there exists a constant C {\displaystyle C} , depending only on Ω {\displaystyle \Omega } and p {\displaystyle p} , so that, for every function u {\displaystyle
Poincaré_inequality
Mathematical function that can be computed by a program
They are the smallest class of partial functions that includes the constant, successor, and projection functions, and is closed under composition, primitive
Computable_function
Mathematical-logic system
the identity function, x ↦ x {\displaystyle x\mapsto x} . Further, λ x . y {\displaystyle \lambda x.y} represents the constant function x ↦ y {\displaystyle
Lambda_calculus
Mathematical function with multiple real-number arguments
real-valued function which has a connected domain, the image is either an interval or a single value. In the latter case, the function is a constant function. The
Function of several real variables
Function_of_several_real_variables
Logarithm to the base of the mathematical constant e
logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal
Natural_logarithm
Topics referred to by the same term
Zero manifold Several terms related to 0 (number): Zero map; see constant function Zero morphism, a kind of morphism in category theory Zero matrix,
0M
S-shaped curve
modeled as a periodic function (of period T {\displaystyle T} ) or (in case of continuous infusion therapy) as a constant function, and one has that 1 T
Logistic_function
Differential equation that is linear with respect to the unknown function
algebraic equations), even when this term is a non-constant function. If the constant term is the zero function, then the differential equation is said to be
Linear_differential_equation
Concept in economics
utility function is a special case of hyperbolic absolute risk aversion and at the same time is the only class of utility functions with constant relative
Isoelastic_utility
Sum of the inverses of the positive cubes
Apéry's constant is a mathematical constant, defined as the infinite sum of the reciprocals of the cubes of the positive integers. In symbols, ζ(3)=∑n=1∞1n3
Apéry's_constant
First known wavelet basis
the function ψ n 2 , k 2 {\displaystyle \psi _{n_{2},k_{2}}} remains constant. It follows in this case that the product of these two Haar functions is
Haar_wavelet
Constants of the mathematical zeta function
In mathematics, the Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted ζ ( s ) {\displaystyle
Particular values of the Riemann zeta function
Particular_values_of_the_Riemann_zeta_function
Mapping arbitrary data to fixed-size values
(collisions). Hash functions rely on generating favorable probability distributions for their effectiveness, reducing access time to nearly constant. High table
Hash_function
Analytic function that does not satisfy a polynomial equation
Euler related it to functions where a constant is raised to a variable exponent, such as the exponential function where the constant base is e. By introducing
Transcendental_function
Branch of mathematics studying functions of a complex variable
range of an entire function f {\displaystyle f} , then f {\displaystyle f} is a constant function. Moreover, a holomorphic function on a connected open
Complex_analysis
Type of mathematical expression
the function that it defines: a constant term and a constant polynomial define constant functions.[citation needed] In fact, as a homogeneous function, it
Polynomial
Generalization of definite integrals to functions of multiple variables
following are some simple methods of integration: When the integrand is a constant function c, the integral is equal to the product of c and the measure of the
Multiple_integral
Number, approximately 0.916
and it is also equal to β(2), where β is the Dirichlet beta function. Catalan's constant was named after Eugène Charles Catalan, who found quickly-converging
Catalan's_constant
Topic in mathematics
this case, we still have L1 convergence to some function, but that function is no longer a constant function. Theorem (general case)—Let ℐ be the sigma-algebra
Asymptotic equipartition property
Asymptotic_equipartition_property
Describes approximate behavior of a function
applications, one chooses the function g(x) appearing within the argument of O(⋅) to be as simple a form as possible, omitting constant factors and lower order
Big_O_notation
Topological space
subspace of the space of continuous functions is the locally constant functions. A function is locally constant if there is a partition of the Cantor
Cantor_space
One of several equivalent definitions of a computable function
zero function as a primitive function that always returns zero, and build the constant functions from the zero function, the successor function and the
General_recursive_function
Complex exponential in terms of sine and cosine
is the constant function of one, so they must be equal (the exponential function is never zero, so this is permitted). Consider the function f(θ) f (
Euler's_formula
Constants in the zeta function's Laurent series expansion
Stieltjes constants are the numbers γk that occur in the Laurent series expansion of the Riemann zeta function: ζ(1+s)=1s+∑n=0∞(−1)nn!γnsn. The constant γ0=γ=0
Stieltjes_constants
This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks
List_of_periodic_functions
Ratio of the perimeter of Bernoulli's lemniscate to its diameter
{\displaystyle 2\varpi } . The lemniscate constant is closely related to the lemniscate elliptic functions and is approximately equal to 2.62205755. It
Lemniscate_constant
Function definition that is not bound to an identifier
anonymous function (function literal, lambda function, or block) is a function definition that is not bound to an identifier. Anonymous functions are often
Anonymous_function
Self-self morphism
a constant function on S has an image that is a proper subset of its codomain, and thus is not bijective (and hence not invertible). The function associating
Endomorphism
Mathematical transform that expresses a function of time as a function of frequency
f(x) ⟷ℱ f^(ξ). For example, the Fourier transform of the delta function is the constant function 1: δ(x) ⟷ℱ 1. When the independent variable (x) represents
Fourier_transform
Concept in mathematics
(2006-10-16). "The generalized-Euler-constant function γ(z) and a generalization of Somos's quadratic recurrence constant". Journal of Mathematical Analysis
K-function
Time constant of an RC circuit
The RC time constant, denoted τ (lowercase tau), the time constant of a resistor–capacitor circuit (RC circuit), is equal to the product of the circuit
RC_time_constant
Mathematical operation on arithmetical functions
=\varepsilon } , the Dirichlet inverse of the constant function 1 {\displaystyle 1} is the Möbius function (see proof). Hence: g = f ∗ 1 {\displaystyle
Dirichlet_convolution
Halting probability of a random computer program
problem. Let PF be the domain of a prefix-free universal computable function F. The constant ΩF is then defined as Ω F = ∑ p ∈ P F 2 − | p | , {\displaystyle
Chaitin's_constant
Type of mathematical function
mathematics, an elementary function is any function of a real or complex variable that can be obtained from constants, algebraic functions, exponentials, and
Elementary_function
Evaluation of a function on its argument
equivalently expressed using function composition as: (f∘g∘h∘j)(x) or even: (f∘g∘h∘j∘x)() if one considers x to be a constant function returning x. In axiomatic
Function_application
Mathematical function with no sudden changes
set is at least T0, then the only continuous functions are the constant functions. Conversely, any function whose codomain is indiscrete is continuous.
Continuous_function
Derivative of a function with multiple variables
derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the
Partial_derivative
Generalized mathematical function
as a multivalued function. The antiderivative of a function is the set of functions whose derivative is that function. The constant of integration follows
Multivalued_function
using simpler functions, especially piecewise linear functions or piecewise constant functions. These are preferred where speed of computation is more
Hard_sigmoid
Continuous deformation between two continuous functions
→ : B n → B n {\displaystyle c_{\vec {0}}:B^{n}\to B^{n}} be the constant function c 0 → ( x ) := 0 → {\displaystyle c_{\vec {0}}(x):={\vec {0}}} which
Homotopy
Derivative of a function
differential coefficient of a function f(x) is what is now called its derivative df(x)/dx, the (not necessarily constant) multiplicative factor or coefficient
Differential_coefficient
Relation between pairs of arithmetic functions
is the unit function ε ∗ 1 = 1, the constant function 1 ∗ 1 = σ0 = d = τ, where d = τ is the number of divisors of n, (see divisor function). Both of these
Möbius_inversion_formula
Concept in complex analysis
real-valued function. The derivative of a constant function is the zero function. Therefore, any constant function is an antiderivative of the zero function. If
Antiderivative (complex analysis)
Antiderivative_(complex_analysis)
the domain of the constant function must be empty, so although the search does not halt it still holds vacuously that the function is a realizer. By the
Markov's_principle
Analytic function in mathematics
mathematics, the Riemann zeta function, or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a function of a complex variable
Riemann_zeta_function
Type of mathematical function
Sawtooth function Floor function Step function, a function composed of constant sub-functions, so also called a piecewise constant function Boxcar function, Heaviside
Piecewise_linear_function
Estimate of time taken for running an algorithm
polynomial in x. An algorithm is termed constant time (often represented as O(1) time) when its complexity function T(n) is bounded by a value that does
Time_complexity
Mathematical theorem in the study of analysis
space and A is a subalgebra of C(X, R) which contains a non-zero constant function. Then A is dense in C(X, R) if and only if it separates points. This
Stone–Weierstrass_theorem
Physical constant relating particle kinetic energy with temperature
The Boltzmann constant (kB or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic
Boltzmann_constant
Algebraic manipulation of "true" and "false"
their outputs are concerned, constants and constant functions are indistinguishable; the difference is that a constant takes no arguments, called a zeroary
Boolean_algebra
Type qualifier denoting the data as being read-only
since C does not have function overloading, and instead, this is handled by having a single function where the input is constant but the output is writable:
Const
Concept in geometry
coordinates. Namely, the area is given by a double integral of the constant function 1 over the disk itself. If D denotes the disk, then the double integral
Area_of_a_circle
power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line Linear function: First degree polynomial,
List of mathematical functions
List_of_mathematical_functions
to itself. Constant function: has a fixed value regardless of its input. Empty function: whose domain equals the empty set. Set function: whose input
List_of_types_of_functions
Constants related to interpolation errors
analysis, Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the interpolant of a function (at the given nodes)
Lebesgue_constant
Whole number
zero function (or zero map) on a domain D. This is the constant function with 0 as its only possible output value, that is, it is the function f defined
0
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CONSTANT FUNCTION
CONSTANT FUNCTION
CONSTANT FUNCTION
CONSTANT FUNCTION
CONSTANT FUNCTION
CONSTANT FUNCTION
CONSTANT FUNCTION
CONSTANT FUNCTION
CONSTANT FUNCTION
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