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Association of one output to each input
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
Function_(mathematics)
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some
List of mathematical functions
List_of_mathematical_functions
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Operation on mathematical functions
In mathematics, the composition operator ∘ {\displaystyle \circ } takes two functions, f {\displaystyle f} and g {\displaystyle g} , and returns a new
Function_composition
Generalization of the concept from statistical mechanics
normalized to one. The normalization for the potential function is the Jacobian for the appropriate mathematical space: it is 1 for ordinary probabilities, and
Partition function (mathematics)
Partition_function_(mathematics)
Divergent sum of positive unit fractions
In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: ∑ n = 1 ∞ 1 n = 1 + 1 2 + 1 3 + 1 4 + 1 5 +
Harmonic_series_(mathematics)
Function whose actual domain of definition may be smaller than its apparent domain
In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly the whole X itself) to Y. The subset S, that
Partial_function
Mathematical function such that every output has at least one input
In mathematics, a surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's
Surjective_function
Generalized function whose value is zero everywhere except at zero
In mathematical analysis, the Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized
Dirac_delta_function
Functions of an angle
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate
Trigonometric_functions
Generalization of the indicator function for classical sets in fuzzy logic
In mathematics, the membership function of a fuzzy set is a generalization of the indicator function for classical sets. In fuzzy logic, it represents
Membership function (mathematics)
Membership_function_(mathematics)
Hyperbolic analogues of trigonometric functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just
Hyperbolic_functions
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Nearest integers from a number
Floor and ceiling functions In mathematics, the floor function is the function that takes a real number x as input and returns the greatest integer less
Floor_and_ceiling_functions
Function equal to cos x + i sin x
In mathematics, cis is a function defined by cis x = cos x + i sin x, where cos is the cosine function, i is the imaginary unit and sin is the sine function
Cis_(mathematics)
Fundamental trigonometric functions
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle:
Sine_and_cosine
Study of mathematical algorithms for optimization problems
interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically
Mathematical_optimization
Arithmetic operation
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no universal notation for tetration, though
Tetration
Conjecture on zeros of the zeta function
problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics In mathematics
Riemann_hypothesis
Generalized mathematical function
In mathematics, a multivalued function, multiple-valued function, many-valued function, or multifunction, is a function that has two or more values in
Multivalued_function
Branch of mathematics
constructive mathematics, a branch of mathematics that insists that proofs of the existence of a number, function, or other mathematical object should
Calculus
Symbol representing a mathematical object
had a big influence on mathematics ever since. Originally, the term variable was used primarily for the argument of a function, in which case its value
Variable_(mathematics)
Branch of mathematics studying functions of a complex variable
traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of a complex variable of
Complex_analysis
Product of numbers from 1 to n
probability theory, and computer science. Much of the mathematics of the factorial function was developed beginning in the late 18th and early 19th
Factorial
Analytic function that does not satisfy a polynomial equation
In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the
Transcendental_function
Function that is continuous everywhere but differentiable nowhere
In mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere
Weierstrass_function
Function in thermodynamics and statistical physics
partition functions can be defined for different circumstances; see partition function (mathematics) for generalizations. The partition function has many
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Collection of mathematical objects
points in space, lines, other geometric shapes, variables, functions, or even other sets. Mathematics typically does not define precisely what constitutes a
Set_(mathematics)
Function with a repeating pattern
illustrated through both common, everyday examples and more formal mathematical functions. Functions that map real numbers to real numbers can display periodicity
Periodic_function
C standard library header file
C mathematical operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions. Different
C_mathematical_functions
Topics referred to by the same term
Function (language), a way of achieving an aim using language Function (mathematics), a relation that associates an input to a single output Function
Function
Inputs for which a function's value is non-zero
In mathematics, the support of a real-valued function f {\displaystyle f} is the subset of the function's domain consisting of those elements that are
Support_(mathematics)
Book on philosophy of mathematics
Mathematics, Form and Function, a book published in 1986 by Springer-Verlag, is a survey of the whole of mathematics, including its origins and deep structure
Mathematics, Form and Function
Mathematics,_Form_and_Function
Field of knowledge
Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical
Mathematics
Branch of mathematics
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure,
Mathematical_analysis
Linear map or polynomial function of degree one
In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose
Linear_function
Function that returns its argument unchanged
In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the
Identity_function
Mathematical functions having established names and notations
Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis
Special_functions
Special mathematical function defined as sin(x)/x
In mathematics, physics and engineering, the sinc function (/ˈsɪŋk/ SINK), denoted by sinc(x), is defined as either sinc ( x ) = sin x x . {\displaystyle
Sinc_function
Extension of the factorial function
\ln(x)} or log e ( x ) {\displaystyle \log _{e}(x)} . In mathematics, the gamma function (represented by Γ {\displaystyle \Gamma } , capital Greek
Gamma_function
Mathematical concept
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists
Inverse_function
Set of all things that may be the input of a mathematical function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ( f ) {\displaystyle \operatorname
Domain_of_a_function
Mathematical function with no sudden changes
mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.
Continuous_function
Process of repeating items in a self-similar way
logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition
Recursion
Inverse functions of sin, cos, tan, etc.
In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions
Inverse trigonometric functions
Inverse_trigonometric_functions
Mathematical function having a characteristic S-shaped curve or sigmoid curve
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the
Sigmoid_function
Linear combination of indicator functions of real intervals
In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of
Step_function
Mathematical function
In mathematics, a function f ( x ) {\displaystyle f(x)} that satisfies a polynomial equation of the form a n ( x ) f ( x ) n + a n − 1 ( x ) f ( x ) n
Algebraic_function
Continuous function that is not absolutely continuous
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in
Cantor_function
Operation in mathematical calculus
comprehensive mathematical framework that both Leibniz and Newton developed. Given the name infinitesimal calculus, it allowed for precise analysis of functions with
Integral
Mathematical function, inverse of an exponential function
exponentiation extends to other mathematical structures as well. However, in general settings, the logarithm tends to be a multi-valued function. For example, the complex
Logarithm
Value approached by a mathematical object
In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. Limits of functions are
Limit_(mathematics)
Complex-differentiable (mathematical) function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood
Holomorphic_function
Special function defined by an integral
In mathematics, the exponential integral E i {\displaystyle \mathrm {Ei} } is a special function on the complex plane. It is defined as one particular
Exponential_integral
Mathematical-logic system based on functions
In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and
Lambda_calculus
Target set of a mathematical function
In mathematics, a codomain or set of destination of a function is a set into which all of the outputs of the function are constrained to fall. It is the
Codomain
Mathematical function
In mathematics, the reciprocal gamma function is the function f ( z ) = 1 Γ ( z ) , {\displaystyle f(z)={\frac {1}{\Gamma (z)}},} where Γ(z) denotes the
Reciprocal_gamma_function
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
Representation of a mathematical function
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
Graph_of_a_function
Mathematical function, denoted exp(x) or e^x
In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is
Exponential_function
Branch of mathematical logic
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining
Reverse_mathematics
2.71828…, base of natural logarithms
number e is a mathematical constant, approximately equal to 2.71828, that is the base of the natural logarithm and exponential function. It is sometimes
E_(mathematical_constant)
Degree of differentiability of a function or map
In mathematical analysis, the smoothness of a function or map describes the extent to which it has derivatives that exist and vary continuously. Given
Smoothness
Counterintuitive mathematical object
those in related sciences) very frequently speak of whether a mathematical object—a function, a set, a space of one sort or another—is "well-behaved". While
Pathological_(mathematics)
Simpler variant of the Riemann zeta function
In mathematics, the Riemann xi function is a variant of the Riemann zeta function, and is defined so as to have a particularly simple functional equation
Riemann_xi_function
Function, homomorphism, or morphism
In mathematics, a map or mapping is a function in its general sense.[vague] These terms may have originated as from the process of making a geographical
Map_(mathematics)
Study of discrete mathematical structures
continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes
Discrete_mathematics
formulas. Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex;
Mathematical_object
Subfield of mathematics
definitions of addition and multiplication from the successor function and mathematical induction. In the mid-19th century, flaws in Euclid's axioms for
Mathematical_logic
Function returning minus 1, zero or plus 1
In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether
Sign_function
Amount of variation between extrema
In mathematics, the oscillation of a function or a sequence is a number that quantifies how much that sequence or function varies between its extreme
Oscillation_(mathematics)
Sequence of program instructions invokable by other software
Event (computing) – Computing state associated with a point in time Function (mathematics) – Association of one output to each input Functional programming –
Function (computer programming)
Function_(computer_programming)
Analytic function in mathematics
The Riemann zeta function or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a mathematical function of a complex variable
Riemann_zeta_function
Continued Fractions for Special Functions. Springer. p. 182. ISBN 978-1-4020-6948-2. Cajori, Florian (1991). A History of Mathematics (5th ed.). AMS Bookstore
List of mathematical constants
List_of_mathematical_constants
Symbolic description of a mathematical object
In mathematics, an expression is an arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can
Expression_(mathematics)
Kind of mathematical function
In mathematics, and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves
Measurable_function
Special mathematical function
In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Lis(z) of order s and argument z. Only
Polylogarithm
Input to a mathematical function
In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. For example
Argument_of_a_function
Real function with secant line between points above the graph itself
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or
Convex_function
Mathematical functions
In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six
Inverse_hyperbolic_functions
1964 mathematical reference work edited by M. Abramowitz and I. Stegun
Technology (NIST). Its full title is Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. A digital successor to the Handbook
Abramowitz_and_Stegun
Point where function's value is zero
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f {\displaystyle f} , is a member x {\displaystyle
Zero_of_a_function
Types of special mathematical functions
In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems
Incomplete_gamma_function
Arithmetic function
Liouville Function". Tokyo Journal of Mathematics. 3 (1): 187–189. doi:10.3836/tjm/1270216093. MR 0584557. Weisstein, Eric W. "Liouville Function". MathWorld
Liouville_function
One-to-one correspondence
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the
Bijection
Topics referred to by the same term
Transformation (function), concerning functions from sets to themselves. For functions in the broader sense, see function (mathematics). Affine transformation
Transformation
Probability distribution
published 1964]. Probability Functions (chapter 26). Handbook of mathematical functions with formulas, graphs, and mathematical tables, by Abramowitz, M.;
Normal_distribution
Well-quasi-ordering of finite trees
result that has also proved important in reverse mathematics and leads to the even-faster-growing SSCG function, which dwarfs TREE. The version given here is
Kruskal's_tree_theorem
Basic notion of sameness in mathematics
In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical
Equality_(mathematics)
Mathematical function characterizing set membership
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all
Indicator_function
Negative of a convex function
In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to
Concave_function
Function that is its own inverse
In mathematics, an involution, involutory function, or self-inverse function is a function f that is its own inverse, f(f(x)) = x for all x in the domain
Involution_(mathematics)
Online collection of special functions from NIST
Mathematical Functions (DLMF) is an online project at the National Institute of Standards and Technology (NIST) to develop a database of mathematical
Digital Library of Mathematical Functions
Digital_Library_of_Mathematical_Functions
Function with a smaller domain
In mathematics, the restriction of a function f {\displaystyle f} is a new function, denoted f | A {\displaystyle f\vert _{A}} or f ↾ A , {\displaystyle
Restriction_(mathematics)
Types of mappings in mathematics
In mathematics, a functional is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the
Functional_(mathematics)
Differentiable function whose derivative is not Riemann integrable
In mathematics, Volterra's function, named for Vito Volterra, is a real-valued function V defined on the real line R with the following curious combination
Volterra's_function
Family of solutions to related differential equations
Mathematics, EMS Press. Wolfram function pages on Bessel J and Y functions, and modified Bessel I and K functions. Pages include formulas, function evaluators
Bessel_function
Function defined by multiple sub-functions
In mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose
Piecewise_function
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Type of function in mathematics
In mathematical analysis, an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex
Analytic_function
FUNCTION MATHEMATICS
FUNCTION MATHEMATICS
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Girl/Female
Tamil
Ankshika | அஂகà¯à®·à¯€à®•à®¾
It’s derived from the root word - anksh that means a fraction. Ankshika means the fraction of the cosmos
Ankshika | அஂகà¯à®·à¯€à®•à®¾
Boy/Male
Indian
Friction
Surname or Lastname
South German
South German : occupational name for an official in charge of the legal auction of property confiscated in default of a fine; such a sale was known in Middle High German as a gant (from Italian incanto, a derivative of Late Latin inquantare ‘to auction’, from the phrase In quantum? ‘To how much (is the price raised)?’).German : metonymic occupational name for a cooper, from Middle High German ganter, kanter ‘barrel rack’.German : variant of Gander 3.English : occupational name for a glover, from Old French gantier, an agent derivative of gant ‘glove’ (see Gant).
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Girl/Female
Indian
It’s derived from the root word - anksh that means a fraction. Ankshika means the fraction of the cosmos
Girl/Female
Afghan, Arabic, Australian, Indian, Muslim
Fiction; Romance; Story
Boy/Male
French Greek
Cyrano de Bergerac was a seventeenth-century soldier and science-fiction writer.
Biblical
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Girl/Female
Bengali, Indian
Fraction of Time
Surname or Lastname
English
English : topographic name for someone who lived by a watercourse or road junction, Old English gelǣt, or a habitational name from Leat in Devon, or The Leete in Essex, named with this element.
Boy/Male
Australian, Vietnamese
Complete; Mathematics
Girl/Female
Hindu, Indian
Fraction of the Cosmos
FUNCTION MATHEMATICS
FUNCTION MATHEMATICS
Boy/Male
Hindu, Indian
Saint
Girl/Female
Arabic, Christian, Indian, Kannada, Muslim
Highest Point on a Mountain
Boy/Male
Indian, Punjabi, Sikh
Embodiment of All
Girl/Female
Tamil
Cover
Girl/Female
Tamil
Victorious
Boy/Male
Indian, Punjabi, Sikh
Saint Lord
Surname or Lastname
English and Irish
English and Irish : variant spelling of Peak.
Girl/Female
British, English, Latin
Essence
Boy/Male
Indian, Punjabi, Sikh
Love of Guru
Surname or Lastname
English (mainly Yorkshire)
English (mainly Yorkshire) : variant of Hooley.
FUNCTION MATHEMATICS
FUNCTION MATHEMATICS
FUNCTION MATHEMATICS
FUNCTION MATHEMATICS
FUNCTION MATHEMATICS
v. t.
To give sanction to; to ratify; to confirm; to approve.
n.
A derived function; a function obtained from a given function by a certain algebraic process.
n.
The act of anointing, smearing, or rubbing with an unguent, oil, or ointment, especially for medical purposes, or as a symbol of consecration; as, mercurial unction.
n.
The office, duties, or functions of a minister, servant, or agent; ecclesiastical, executive, or ambassadorial function or profession.
v. i.
Alt. of Functionate
v. t.
To separate by means of, or to subject to, fractional distillation or crystallization; to fractionate; -- frequently used with out; as, to fraction out a certain grade of oil from pretroleum.
n.
The course of action which peculiarly pertains to any public officer in church or state; the activity appropriate to any business or profession.
v. t.
The act of uniting, or the state of being united; junction.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
n.
The place or point of union, meeting, or junction; specifically, the place where two or more lines of railway meet or cross.
n.
The natural or assigned action of any power or faculty, as of the soul, or of the intellect; the exertion of an energy of some determinate kind.
n.
The act of feigning, inventing, or imagining; as, by a mere fiction of the mind.
a.
Pertaining to, or connected with, a function or duty; official.
a.
Pertaining to the function of an organ or part, or to the functions in general.
v. t.
To supply with an organ or organs having a special function or functions.
v. t.
To sell by auction.
n.
The act of anointing, or the state of being anointed; unction; specifically (Med.), the rubbing of ointments into the pores of the skin, by which medicinal agents contained in them, such as mercury, iodide of potash, etc., are absorbed.
n.
The act of joining, or the state of being joined; union; combination; coalition; as, the junction of two armies or detachments; the junction of paths.
n.
The things sold by auction or put up to auction.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.