(mathematical analysis) Given a power series f(x)=∑ₙ₌₀ ᪲a_nxⁿ that is convergent for real x in the open interval (0, 1), the value lim _(x→1⁻)∑ₙ₌₀ ᪲a_nxⁿ, which is assigned to f(1)=∑ₙ₌₀ ᪲a_n by the Abel summation method (or A-method).

(mathematical analysis, dated or historical) Ricci calculus; the rules of index notation and manipulation for tensors and tensor fields, as developed by Gregorio Ricci-Curbastro.

(algebra, archaic, of an equation) Having different powers of the unknown quantity in its various terms.

(computing, slang, countable) Any elaborate transformation process or algorithm.

(mathematics, statistics) A discipline within mathematical statistics in which algebra is used to describe and analyse problems;

(mathematics, computing) The subdiscipline of informatics or computer science that studies algorithms.

(mathematics) Any function in which the interchange of two independent variables changes the sign of the dependent variable.

(uncountable, mathematics) The mathematical study of functions, sequences, series, limits, derivatives and integrals.

(mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.

(mathematical analysis) The practice of extending analytic functions.

(mathematical analysis) Any smooth (infinitely differentiable) function f, defined on an open set D⊆ℂ( textit or⊆ℝ), whose value in some neighbourhood of any given point x_0∈D is given by the Taylor series ∑ₙ₌₀ ᪲(f⁽ⁿ⁾(x_0))/(n!)(x-x_0)ⁿ.

(mathematics, physics) The application of calculus to classical mechanics.

A function F(x) is the antidifference of f(x) if F(x+1)-F(x)=f(x).

(calculus) The process of finding the antiderivative.

(mathematics) A local minimum on a graph

(mathematical analysis) A sequence in which each term except the first is obtained from the previous by adding a constant value, known as the common difference of the arithmetic progression.

(mathematics) The treatment of mathematics by methods involving only the fundamental concepts and operations of arithmetic.

(set theory) Of a relation R on a set S: having the property that for any two elements of S (not necessarily distinct), at least one is not related to the other via R.

(mathematical analysis) Coming into consideration as a variable tends to a limit, usually infinity.

(mathematical analysis) Del.

(mathematics, computing) The automatic differentiation of a function by a computer.

(mathematics, computing) Exact differentiation of functions represented in program code by inspecting the code (as opposed to mere evaluation) and repeated application of the chain rule.

(mathematics) A number raised to the power of an exponent.

A differential operator having two arguments.

(probability theory, statistics) The discrete probability distribution of the number of successes in a sequence of n independent trials, each of which yields success with probability p.

(algebra) With respect to a Boolean variable x_i: The XOR-sum of the positive and negative Shannon cofactors of the given derived function with respect to x_i. In symbols: ∂f/∂x_i(⃑x)=f_x_i(⃑x)⊕f_̄x_i(⃑x).

(mathematical analysis) A function which is Borel measurable.

(mathematical analysis) A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space.

(mathematics) Any function whose values remain bounded by some constant.

(mathematics) Any function whose value is zero except for a finite part of its argument for which it has a constant non-zero value

(mathematics) A function that is right continuous and has a left limit.

(countable, mathematics) Any formal system in which symbolic expressions are manipulated according to fixed rules.

(calculus) The form of calculus that deals with the maxima and minima of definite integrals of functions of many variables.

(mathematical analysis) Any sequence x_n in a metric space with metric d such that for every 𝜀>0 there exists a natural number N such that for all k,m>N, d(x_k,x_m)<𝜀.

(mathematics) A function that maps a real number to the smallest integer that is no smaller than it.

(calculus) A formula for computing the derivative of the functional composition of two or more functions.

(mathematics, probability theory) A complex function completely defining the probability distribution of a real-valued random variable

(set theory) A function whose domain is a family of nonempty sets, and which selects a member from each of those sets as its value.

(mathematics) an interval in the real number line which contains its supremum and infimum.

(computing) A variable declared with a codimension.

(mathematics, of a subset) Having an element b for each element a in the superset such that b is less than or equal to a.

(mathematics) Either of a pair of functions that have the same domain and that the values of one are equal to or greater than the other for all points in that domain.

(mathematics) The replacement of a set by its complement

(mathematics) The unary operation which maps complex numbers to their complex conjugates.

(mathematics, arithmetic) Any fraction in which either or both of the numerator or denominator are themselves fractions.

(mathematics) A function of a function.

(mathematics) A function of one or more independent variables, at least one of which is itself a function of one or more other independent variables; a function of function(s).

(mathematics, optimisation theory, of a function on a set) For a given set S⊆ℝⁿ and real-valued function f defined on the convex hull conv(S), the lowest-valued concave function that overestimates or equals f over S.

(mathematics) A function whose value is the same for all the elements of its domain.

(calculus) An unspecified constant term added to a particular antiderivative to make it represent its whole family of antiderivatives, usually denoted with C.

(mathematics) The integral of a function around a contour on the complex plane.

(mathematical analysis) An infinite series whose partial sums converge

(mathematics, functional analysis) A mathematical operation on two functions that produces a third that expresses how the shape of one is modified by the other; the integral of the product of the two functions after one is reflected about the y-axis and shifted along the x-axis.

(mathematical analysis) A positive measure which, for each subset of a given measure space, assigns a value equal to the number of points in that subset.

(object-oriented programming) Using or relating to covariance.

(mathematics) Any function, in the calculus of variations, that satisfies the Euler equations

(mathematics, obsolete) An invariant function of a differential equation

Alternative form of cadlag [(mathematics) A function that is right continuous and has a left limit.]

(mathematics) Any function of a real variable whose value decreases (or is constant) as the variable increases.

(mathematics) The integral of a function between an upper and lower limit

(mathematical analysis) The symbol ∇ used to denote the gradient operator.

(mathematics) The operation of deducing one function from another according to a fixed definition, referred to as derivation or differentiation; this is the inverse operation to integration.

(Of a function of a single variable f(x)) The derived function of f(x): the function giving the instantaneous rate of change of f; equivalently, the function giving the slope of the line tangent to the graph of f. Written f'(x) or (df)/(dx) in Leibnitz's notation, ̇f(x) in Newton's notation (the latter used particularly when the independent variable is time).

(mathematics) The expression of a function in the form of a series.

(mathematics) Describing a function that is analytic or antianalytic with regards to both the domain and codomain

(mathematics, informal) A college course in differential equations, usually as part of a standardized calculus curriculum.

(mathematics) more broadly, any recurrence relation

(mathematical analysis) The slope of a secant as obtained by dividing the vertical difference between two intersections of the secant and a curve with their horizontal distance. When the horizontal distance approaches zero the slope of the secant approaches the derivative of the curve.

(combinatorics) A subset of a group such that any element of the group can be expressed as the difference (or the quotient) of two elements in such subset.

(calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.

(mathematics) An infinitesimal change in a variable, or the result of differentiation.

(calculus) The calculus that deals with instantaneous rates of change.

(calculus) an equation involving the derivatives of a function

(mathematics, fractional calculus) Any type of mathematical operator which combines the properties of the fractional derivative and the fractional integral.

(mathematics) The first of the polygamma functions, being the logarithmic derivative of the gamma function.

(mathematics) A periodic tempered distribution constructed from Dirac delta functions for some given period. It allows both continuous and discrete phenomena to be represented in a single framework.

(mathematics) A function-like symbol denoted as δ, with the property ∫f(t)𝛿(x-t)dt=f(x), informally understood as a function with an infinite value at 0 and zero elsewhere, and formally as a distribution or a measure.

(mathematics) Having at most one fewer zeros (including multiplicities) than the dimension of the problem space.

(mathematics) A family of sets sharing no elements in common; sets whose intersection is the empty set.

(mathematics) A property of functions that have a rule describing how the function can be performed to the individual components of another operation.

(set theory) One of the objects in a set.

(mathematics) A function whose codomain is equal to its domain.

(mathematics) An approach to mathematical analysis using the epsilon-delta definition of a limit, i.e. with explicit estimation of error bounds, as opposed to using infinitesimals.

(mathematics) Of two sets, having a bijection with one another.

(mathematics) Any function whose value is unchanged if the independent variable changes sign i.e. f(x) = f(-x)

(mathematics) Any function whose value may be directly calculated from the independent variable.

A rule-of-thumb technique for smoothing time series data using the exponential window function.

(calculus) A differential operator which acts on a differential k-form to yield a differential (k+1)-form, unless the k-form is a pseudoscalar, in which case it yields 0.

(mathematics) The process of factorization.

(mathematics) A function in a system of differential equations that is only a function of time, unaffected by the other variables; or, more generally, any non-homogeneous source function in any variable.

(mathematics) fractal analysis or analytics

(mathematical analysis, uncountable) The branch of mathematics that studies generalisations of calculus to allow noninteger (i.e., real or complex) powers of the differentiation operator D and the integration operator J; (countable) any one of said generalisations of calculus.

(mathematics, logic) A variable (occurring within some expression or well-formed formula) which is not bound by a quantifier or analogous symbol (such as a lambda abstractor, the "differential d" near the end of an integral or differential form, or a summation symbol).

(mathematics) A function that takes a function as its argument; More precisely: A function y=f(x) whose argument x varies in a space of (real or complex valued) functions and whose value belongs to a monodimensional space. An example is the definite integration of integrable real functions in a real interval.

(mathematical analysis) A meromorphic function which generalizes the notion of factorial to complex numbers and has singularities at the nonpositive integers; any of certain generalizations or analogues of said function, such as extend the factorial to domains other than the complex numbers.

(mathematics) A function of the form f(x)=a· exp (-((x-b)²)/(2c²)) for arbitrary real-number constants a, b and non-zero c; used in statistics, signal processing, etc.

(mathematics) A continued fraction were the numerators and denominators can assume arbitrary values.

(computing) The observation that computing power increases as the square of the cost, e.g. a computer that costs twice as much ought to be four times as fast.

(mathematics) A method of regularizing divergent integrals by dropping some divergent terms and keeping the finite part.

(signal processing) A discrete window function, w(n)=1/2;(1- cos ((2𝜋n)/(N-1))), typically used to select a subset of a series of samples in order to perform a Fourier transform or other calculation.

(mathematical analysis) A study of the representation of functions or signals as the superposition of basic waves, involving the notions of harmonic functions, trigonometric series, Fourier series, Fourier transforms, almost periodic functions, and others.

(mathematics) a function f(x) which has the property that for any c, f(cx)=cf(x).

(probability theory, statistics) A discrete probability distribution that describes the probability of k "successes" in a sequence of n draws without replacement from a finite population.

(mathematics, computing) (said of a function) Such that, when performed multiple times on the same subject, it has no further effect on its subject after the first time it is performed.

(mathematical analysis, algebraic geometry) A function defined by a (multivariable) implicit equation when one of the variables is regarded as the value of the function, especially where said equation is such that the value is not directly calculable from the other variables.

(mathematics) An integral where at least one of the endpoints is taken as a limit, either to a specific number or to infinity.

(mathematics) Any generalized function which is defined by its behavior under integration.

(calculus, of a vector field) Having a divergence equal to zero.

(mathematics) A function whose derivative is a given function; an antiderivative

(mathematics) Any of a set of functions the value of which can not be deduced from that of all the others.

A function which is equal to 1 for all points in its domain which belong to a given set, and is equal to 0 for all points in the domain which do not belong to that given set.

(mathematics, mathematical analysis) a systematic employment of infinitesimals that reduces calculus to algebra; nonstandard analysis.

(calculus) the problem of solving a (set of) ordinary differential equations accompanied by the requirement that the function sought (and possibly also one or more of its derivatives), taken for some value, equals some other specific value; graphically, (for example) the problem of finding that antiderivative of some function that passes through a particular point

(mathematics) A relation on sets (X,Y) that associates each element of Y with at most one element of X.

(mathematics) Any function that possesses a finite integral

(mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;

(calculus) The calculus that generalizes summation to find areas, masses, volumes, sums, and totals of quantities described by continuously varying functions.

(mathematics) An entire function

(calculus) The function that is to be integrated

(mathematics) A device that determines the value of an integral by measuring the area under a curve (and drawing the curve of its integral)

(calculus) The operation of finding the integral of a function.

(mathematical analysis) A method of integration directly related to the rule for differentiation of products; can be written as ∫udv=uv-∫vdu.

(calculus) A theorem that states for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value.

(mathematics) Unaffected by a specified operation (especially by a transformation)

(mathematics) A differentiable function ƒ from Rⁿ to R is invex if there exists a vector valued function g such that f(x)-f(u)≥g(x,u)·∇f(u),, for all x and u.

(number theory, of a fraction) Whose numerator and denominator share no common factor greater than 1.

(mathematics) A discontinuity in the graph of a function, where the function is continuous in a punctured interval of the discontinuity.

(mathematics) Any of class of special functions, usually denoted as two pairs of functions berₙ(x), beiₙ(x), kerₙ(x) and keiₙ(x) with variable x and given order number n. The former two functions berₙ(x) and beiₙ(x) respectively correspond to the real part and the imaginary part of the Kelvin differential equation's solution that can be expressed with the Bessel function of the first kind Jₙ(x), and the latter kerₙ(x) and keiₙ(x) correspond to those that can be expressed with the modified Bessel function of the second kind Kₙ(x).

(calculus) A function used to define an integral transform.

(computing) A randomized algorithm that always gives a correct result rather than merely giving a probably correct result.

(mathematical analysis, singular only, definite and countable) An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range. (Formal definitions can be found at PlanetMath).

(mathematical analysis) A unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides).

(mathematics) algebraic expressions whose literal coefficients represent the same value regardless of the numbers assigned to them.

(mathematics) (Of a real-valued real function f) Such that there exists a constant K such that whenever x_1 and x_2 are in the domain of f, |f(x_1)-f(x_2)|≤K|x_1-x_2|.

(mathematical analysis) A strong form of uniform continuity for functions.

(calculus, mathematical analysis) Given a real or complex function f, the ratio of the value of the derivative to the value of the function, (f')/f, regarded as a function.

The ratio of the Laplace transform of the primary feedback signal of a control system to that of the actuating signal

(mathematics, order theory) A subset of a poset which contains any descending chain which starts at any element of itself.

(mathematics) The mathematical study of functions, sequences, series, limits, derivatives and integrals.

(mathematics) A set together with a collection of mathematical objects such as other sets, relations or operations which endow it with additional structure.

(calculus, uncountable) The theorem that for any real-valued function that is differentiable on an interval, there is a point in that interval where the derivative of the curve equals the slope of the straight line between the graphed function values at the interval's end points.

(mathematics) Any well-behaved function of real numbers between measurable spaces.

(mathematics) A branch of mathematical analysis, concerned with the theory of integration, that generalizes the intuitive notions of length, area and volume.

(mathematics) A generalization of the indicator function for a fuzzy set which assigns a truth value (0 or 1) to each element.

Initialism of moment-generating function. [(mathematics) A function derived from the probability distribution of a random variable.]

(complex analysis) Any of several variations of the Borel summation method for summing possibly divergent formal power series.

(mathematics) An "approximation to the identity", a smooth function with special properties, used in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution.

(calculus) A function f : X→R (where X is a subset of R, possibly a discrete set) that either never decreases or never increases as its independent variable increases; that is, either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x).

(mathematics) The study of differentiable functions, where the domain of each is a manifold and the codomain is the real line.

(mathematics) A method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

(mathematics) A vector that has no invariants.

(mathematics, computing) The study of numerical analysis algorithms to obtain approximate values of definite integrals.

(calculus) The study of calculus from the perspective of the theory of operators.

(mathematics) A function or other mapping that carries variables defined on a domain into another variable or set of variables in a defined range.

(mathematics) The sequence in which the various operations in a mathematical expression are to be evaluated.

(mathematics) (of a function) defined for each point x in the domain of the function by inf diam(f(U))∣Uisaneighborhoodofx, and describes the difference (possibly ∞) between the limit superior and limit inferior of the function near that point.

(mathematical analysis, measure theory) A measure-like function derived from some premeasure as follows: when it is applied to a set E, it yields the infimum of the premeasures of all possible premeasurable covers of E. More abstractly, a measure-like function whose domain is the power set of some underlying set, which has the properties of (1) yielding zero when applied to the empty set, (2) being monotonic (if A is subset of B then this function applied to A is less-than-or-equal to this function applied to B), (3) being subadditive (if A is a countable sum of Bⱼ's then this function applied to A is less-than-or-equal to the sum of the applications of this function to the Bⱼ's).

(obsolete, mathematics) The division of the terms of an equation by a known quantity that is involved in the first term.

(mathematics) A partial derivative: a derivative with respect to one independent variable of a function in multiple variables while holding the other variables constant.

(mathematics) an infinitesimal change in a variable in a partial derivative, or the result of partial differentiation

(calculus) A differential equation that involves the partial derivatives of a function of several variables.

(mathematics) A function whose domain is a subset of the set on which it is formally defined; i.e., a function f: X→Y for which values f(x) are defined only for x ∈ W, where W ⊆ X.

(mathematics) Any solution to a differential equation.

(mathematical analysis) Initialism of partial differential equation. [(calculus) A differential equation that involves the partial derivatives of a function of several variables.]

(mathematics) A continued fraction with a sequence of numerators and denominators that repeat indefinitely

Initialism of probability mass function. [(mathematics) A function that gives the relative probability that a discrete random variable is exactly equal to some value.]

(mathematics) Any function whose values are points

(mathematics) Of an algorithm, which terminates in polynomial time.

(convex analysis) A particular inequality about convex functions, similar to Jensen's inequality.

Alternative spelling of preexponent [(mathematics) Any factor that multiplies an exponential function]

(statistics) An approximation to the joint probability distribution of a collection of random variables.

(mathematics) A generalization of a theorem, identity or expression that involves a new parameter q that returns the original theorem, identity or expression in the limit as q → 1. They have applications in the study of fractals and the entropy of chaotic dynamical systems.

(mathematics) Belonging or relating to a generalization of the class of real analytic functions based upon the fact that, if f is an analytic function on an interval [a,b] ⊂ R, and at some point f and all of its derivatives are zero, then f is identically zero on all of [a,b].

In computational learning theory, a measure of the richness of a class of real-valued functions with respect to a probability distribution.

(mathematics) The branch of mathematics dealing with the real numbers and related structures.

(mathematics) an equation that recursively defines a sequence; each term of the sequence is defined as a function of the preceding terms.

(mathematics, not comparable) of an expression, each term of which is determined by applying a formula to preceding terms

(mathematics) Any function whose value may be obtained using a finite number of operations using a precisely specified algorithm.

(mathematics, of a polynomial) Able to be factored into polynomials of lower degree, as x²-1.

(fuzzy logic) A binary function from [0,1] × [0,1] to [0,1] which is defined in terms of the t-norm as follows: x→y= sup z|z*x⩽y, where * denotes the t-norm function and sup denotes the supremum.

(mathematics) A generalization of the Riemann integral, serving as a precursor of the Lebesgue integral and a means of unifying equivalent forms of statistical theorems that apply to discrete and continuous probability.

(mathematics) A quantity that has magnitude but not direction; compare vector.

(mathematics) A kind of fraction. If (h_n-1)/(k_n-1), (h_n)/(k_n) are successive convergents, then any fraction of the form (h_n-1+ah_n)/(k_n-1+ak_n), where a is a nonnegative integer and the numerators and denominators are between the n and n+1 terms inclusive, is a semiconvergent.

(mathematics) Related to a differential equation and its criticoids.

(mathematics) A function that assigns a non-negative number to each element of a set that is subadditive.

(game theory) A function on a vector space of all coalitional games which verifies linearity, anonymity, positivity, and inessential games.

(calculus) a constant that may be introduced upon separation of variables

(mathematical analysis, statistics) Any of various real functions whose graph resembles an elongated letter "S"; specifically, the logistic function y=(eˣ)/(eˣ+1)=1/(1+e⁻ˣ).

(mathematical analysis) Any complex-valued measurable function whose range is finite.

(mathematics) Any of several approximations for definite integrals.

(mathematics) Of a function, associating a unique value of its range with each value of its domain.

(mathematics) a function that has derivatives of all finite orders everywhere in its domain.

Any of various specific mathematical functions that have more or less established names and notations due to their importance.

(mathematics) A function from the real line to a finite subset of the real line.

(calculus) a type of differential equation in which one or more of the terms is a stochastic process resulting in a solution which is itself a stochastic process

(mathematics) Any function of a real variable whose value decreases as the variable increases.

(mathematics) One component of an algebra or graph that is made up of the union of several subalgebras or subgraphs.

(mathematics) A generalization of the notion of a derivative, defined as the slope of a line that either touches, or is everywhere below the line of a convex function.

(mathematics) The formation of a subderivative

(mathematics) An equation that forms part of another.

(mathematics) Having a lesser constant value than a related level set

(chemistry) A subset of a combinatorial library (collection of compounds generated using combinatorial chemistry)

(mathematics)

(mathematics)

(mathematics) A set of infinite words representing the evolution of a discrete system, used in symbolic dynamics.

(mathematical analysis) A summation method.

(mathematics, of a function) Such that the image of a sum is at least the sum of the images of the summands.

(mathematics) Very rapid convergence

(mathematics) A derivation within a superalgebra

(mathematics) Having a superderivative.

(mathematics, programming) An expression that contains multiple subexpressions.

(mathematics) An iterative form of optimization.

(mathematics) An integral over a 2-dimensional domain

(mathematics, set theory) To form or to undergo surjection

(fuzzy logic) A binary function from [0,1] × [0,1] to [0,1], which, when given (a,b) as input, returns one minus a t-norm of (1 − a, 1 − b).

(calculus) A method to simplify integration by parts that precalculates the necessary derivatives and antiderivatives in a table.

(mathematics, physics) The set of values, representing time, over which a function dependent on time is defined.

(mathematics) A function.

(mathematics) a mathematical representation of the relation between the input and output of a linear time-invariant system

(mathematics) The replacement of the variables in an algebraic expression by their values in terms of another set of variables; a mapping of one space onto another or onto itself; a function that changes the position or direction of the axes of a coordinate system.

(graph theory, of a graph) Such that, for any two vertices there exists an automorphism which maps one to the other.

(calculus) A method of integration in which a function of a variable is replaced with a new variable, conventionally called u.

(mathematics) Describing any discrete system whose dependent variables also take discrete values

(mathematics, of a set, whose subsets are partially ordered by inclusion) A proper filter which has a law of dichotomy for complements.

(mathematical analysis, of a function) The property of being uniformly continuous.

(countable) An algebraic structure studied therein.

(mathematical analysis) The upper limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the "first subsequence." Then remove the first term of the first subsequence in order to obtain the "second subsequence." Repeat the removal of first terms in order to obtain a "third subsequence," "fourth subsequence," etc. Find the supremum of each of these subsequences, then find the infimum of all of these supremums. This infimum is the upper limit.

(mathematics) A fraction which reduces to the form 0/0 for a particular value of the variable which enters it, usually in consequence of the existence of a common factor in both terms of the fraction, which factor becomes 0 for this particular value of the variable.

A model for nonlinear behavior similar to the Taylor series, differing in its ability to capture 'memory' effects.

(mathematics) An integral over a 3-dimensional domain.

(mathematics) A certain arithmetic function that is neither multiplicative nor additive. It is denoted by Λ(n) and defined as :𝛬(n)= log p mbox ifn=pᵏ mbox forsomeprimep mbox andintegerk>1,\0 mbox otherwise.

(mathematics) A real-valued function that is continuous everywhere but differentiable nowhere.

(set theory, measure theory, probability theory) A non-empty collection of subsets of a given set Ώ that is closed under non-empty finite intersections.

(mathematical analysis) countable additivity