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mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member
Integer-valued_function
Nearest integers from a number
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 than
Floor_and_ceiling_functions
Topics referred to by the same term
Integer function may refer to: Integer-valued function, an integer function Floor function, sometimes referred as the integer function, INT Arithmetic
Integer_function
Number in {..., –2, –1, 0, 1, 2, ...}
a positive integer Complex integer Hyperinteger Integer complexity Integer lattice Integer part Integer sequence Integer-valued function Mathematical
Integer
Function returning one of only two values
a Boolean function is a k-ary integer-valued function giving the correlation between a certain set of changes in the inputs and the function output. For
Boolean_function
Family of solutions to related differential equations
is an integer or a half-integer. When α {\displaystyle \alpha } is an integer, the resulting Bessel functions are often called cylinder functions or cylindrical
Bessel_function
Mathematical constants
gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer, half-integer, and some
Particular values of the gamma function
Particular_values_of_the_gamma_function
Extension of the factorial function
OEIS. The values presented here are truncated rather than rounded.) The complex-valued gamma function is undefined for non-positive integers, but in these
Gamma_function
Generalized mathematical function
a multivalued function, multiple-valued function, many-valued function, or multifunction, is a function that has two or more values in its range for
Multivalued_function
Function in mathematical number theory
a branch of mathematics, the Carmichael function λ(n) of a positive integer n is the smallest positive integer m such that a m ≡ 1 ( mod n ) {\displaystyle
Carmichael_function
Polynomial with integer value for integer input
mathematics, an integer-valued polynomial (also known as a numerical polynomial) P ( t ) {\displaystyle P(t)} is a polynomial whose value P ( n ) {\displaystyle
Integer-valued_polynomial
Constants of the mathematical zeta function
It also includes derivatives and some series composed of the zeta function at integer arguments. The same equation in s {\displaystyle s} above also holds
Particular values of the Riemann zeta function
Particular_values_of_the_Riemann_zeta_function
Functions such that f(–x) equals f(x) or –f(x)
n is an odd integer. Even functions are those real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose
Even_and_odd_functions
Function that is continuous everywhere but differentiable nowhere
mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere
Weierstrass_function
Method to solve optimization problems
is defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polytope. A linear programming algorithm
Linear_programming
Replacing a number with a simpler value
especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines;
Rounding
Mapping arbitrary data to fixed-size values
(reinterpreted as an integer) as the hashed value. The cost of computing this identity hash function is effectively zero. This hash function is perfect, as
Hash_function
Number of integers coprime to and less than n
_{e}(x)} . In number theory, Euler's totient function counts the positive integers up to a given integer n {\displaystyle n} that are relatively prime
Euler's_totient_function
Types of special mathematical functions
the domain C of multi-valued functions by a suitable manifold in C × C called Riemann surface. While this removes multi-valuedness, one has to know the
Incomplete_gamma_function
Data types supported by the C programming language
and false. _Bool functions similarly to a normal integer type, with one exception: any conversion to a _Bool gives 0 (false) if the value equals 0; otherwise
C_data_types
Analytic function in mathematics
Riemann sphere the zeta function has an essential singularity. For sums involving the zeta function at integer and half-integer values, see rational zeta series
Riemann_zeta_function
Association of one output to each input
scalar-valued or vector-valued functions, which share a specific property and form a topological vector space. For example, the real smooth functions with
Function_(mathematics)
Quickly growing function
function (which had three non-negative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function"
Ackermann_function
Number of partitions of an integer
partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has the
Partition function (number theory)
Partition_function_(number_theory)
Degree of differentiability of a function or map
smoothness of a function or map describes the extent to which it has derivatives that exist and vary continuously. Given a non-negative integer k {\displaystyle
Smoothness
Function with a multiplicative scaling behaviour
degree of homogeneity, or simply the degree. That is, if k is an integer, a function f of n variables is homogeneous of degree k if f ( s x 1 , … , s
Homogeneous_function
Online database of integer sequences
The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Type of function in mathematics
{\displaystyle 0} changes its value by an integer multiple of 2 π i {\displaystyle 2\pi i} . For this reason, a single-valued branch of the logarithm can
Analytic_function
Function representing the number of primes less than or equal to a given number
shows how the three functions π(x), x/log x, and li(x) compared at powers of 10. See also, and In the On-Line Encyclopedia of Integer Sequences, the π(x)
Prime-counting_function
Function on an integer n which is log(p) if n equals p^k and zero otherwise
Mangoldt function, denoted by Λ ( n ) {\displaystyle \Lambda (n)} , is defined as Λ ( n ) = { log p if n = p k for some prime p and integer k ≥ 1
Von_Mangoldt_function
Computer arithmetic error
computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the range
Integer_overflow
Datum of integral data type
negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping varies so the set of integer sizes
Integer_(computer_science)
Property of functions which is weaker than continuity
semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f {\displaystyle f} is upper (respectively
Semi-continuity
Inverse functions of sin, cos, tan, etc.
-\arctan(x)}{\pi }}\right)\,.} The function rni {\displaystyle \operatorname {rni} } rounds to the nearest integer. For angles near 0 and π, arccosine
Inverse trigonometric functions
Inverse_trigonometric_functions
Function of a knot that takes the same value for equivalent knots
invariants can be defined by considering some integer-valued function of knot diagrams and taking its minimum value over all possible diagrams of a given knot
Knot_invariant
Non-cryptographic hash function
unsigned integer. The FNV_offset_basis is the 64-bit value: 14695981039346656037 (in hex, 0xcbf29ce484222325). The FNV_prime is the 64-bit value 1099511628211
Fowler–Noll–Vo_hash_function
Concept in probability theory and statistics
theory and statistics, the moment generating function of a real-valued random variable is a generating function that provides an alternative specification
Moment_generating_function
Whose values lie in an infinite-dimensional vector space
Such functions are applied in most sciences including physics. Set f k ( t ) = t / k 2 {\displaystyle f_{k}(t)=t/k^{2}} for every positive integer k {\displaystyle
Infinite-dimensional vector function
Infinite-dimensional_vector_function
Computational operation
a and n both being integers, many computing systems now allow other types of numeric operands. The range of values for an integer modulo operation of
Modulo
Functions of an angle
\sin(x+y).} A positive integer appearing as a superscript after the symbol of the function denotes exponentiation, not function composition. For example
Trigonometric_functions
Mathematical function, inverse of an exponential function
tends to be a multi-valued function. For example, the complex logarithm is the multi-valued inverse of the complex exponential function. Similarly, the discrete
Logarithm
This is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. OEIS core sequences Index to
List_of_integer_sequences
Branch of mathematics studying functions of a complex variable
real-valued. In other words, a complex function f : C → C {\displaystyle f:\mathbb {C} \to \mathbb {C} } may be decomposed into two real-valued functions (
Complex_analysis
Arithmetic operation
integer, the identities are valid for all nonzero complex numbers. If exponentiation is considered as a multivalued function then the possible values
Exponentiation
Probability that random variable X is less than or equal to x
cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} ,
Cumulative distribution function
Cumulative_distribution_function
Mathematical function whose derivative exists
or complex function of a single variable is differentiable if its derivative exists at each point in its domain. For real-valued functions of a real variable
Differentiable_function
Function that is discontinuous at rationals and continuous at irrationals
Thomae's function is a real-valued function of a real variable that can be defined as: f ( x ) = { 1 q if x = p q ( x is rational), with p ∈ Z and
Thomae's_function
Fast-growing function
function is a mathematical function defined by Harvey Friedman. It is defined by SSCG ( k ) {\displaystyle {\text{SSCG}}(k)} as the largest integer n
Friedman's_SSCG_function
Multivalued function in mathematics
each integer k {\displaystyle k} there is one branch, denoted by W k ( z ) {\displaystyle W_{k}\left(z\right)} , which is a complex-valued function of one
Lambert_W_function
Arithmetic function related to the divisors of an integer
theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number
Divisor_function
simple reflection has length one. The function l is then an integer-valued function of W; it is a length function of W. It follows immediately from the
Length of a Weyl group element
Length_of_a_Weyl_group_element
Type of mathematical function
sheaves of locally constant functions on X . {\displaystyle X.} To be more definite, the locally constant integer-valued functions on X {\displaystyle X} form
Locally_constant_function
Decomposition of an integer as a sum of positive integers
partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only
Integer_partition
Number-theoretical function
theory, the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n {\displaystyle n} as
Sum_of_squares_function
Function whose domain is the positive integers
arithmetical, or number-theoretic function is generally any function whose domain is the set of positive integers and whose range is a subset of the
Arithmetic_function
Ordered list of whole numbers
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula
Integer_sequence
C standard library header file
mathematical functions, which use floating-point numbers, are defined in <math.h> (<cmath> header in C++). The functions that operate on integers, such as
C_mathematical_functions
Mathematical function
and γ is the Euler–Mascheroni constant. For half-integer arguments the digamma function takes the values ψ ( n + 1 2 ) = − γ − 2 ln 2 + ∑ k = 1 n 2 2
Digamma_function
Logarithm to the base of the mathematical constant e
the values being expressed as integers. The natural logarithm can be defined more generally as the inverse function of the exponential function e x {\displaystyle
Natural_logarithm
the 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
Mathematical optimization problem restricted to integers
are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints
Integer_programming
Special mathematical function defined as sin(x)/x
normalized sinc function are the nonzero integer values of x. The function has also been called the cardinal sine or sine cardinal function. The term "sinc"
Sinc_function
Root of a quadratic polynomial with a unit leading coefficient
theory, quadratic integers are a generalization of the usual integers to quadratic fields. A complex number is called a quadratic integer if it is a root
Quadratic_integer
Number
unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other
0
Product of numbers from 1 to n
factorial function to a continuous function of complex numbers, except at the negative integers, the (offset) gamma function. Many other notable functions and
Factorial
Number with a real and an imaginary part
numbers are often used to compute certain real-valued improper integrals, by means of complex-valued functions. Several methods exist to do this; see methods
Complex_number
Point of interest for complex multi-valued functions
point of a multivalued function is a point such that if the function is n {\displaystyle n} -valued (has n {\displaystyle n} values) at that point, all of
Branch_point
Generalization of the Riemann zeta function for algebraic number fields
Riemann zeta function ζ ( s ) {\displaystyle \zeta (s)} represents information about the factorization of integers. Dedekind zeta functions generalize many
Dedekind_zeta_function
positive integers <= 17 Egyptian fraction 1013 = Sophie Germain prime, centered square number, Mertens function zero 1014 = 210-10, Mertens function zero
1000_(number)
Integers have unique prime factorizations
factorization theorem and prime factorization theorem, states that every integer greater than 1 is either prime or can be represented uniquely as a product
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Classes of data types
value type) into an Integer object (an object type), or reversing this via "unboxing". Even when function arguments are passed using "call by value"
Value_type_and_reference_type
Numeral system using the values -1, 0 and 1
in place of T . {\displaystyle \operatorname {T} .} Define an integer-valued function f = f D 3 : D 3 → Z {\displaystyle f=f_{{\mathcal {D}}_{3}}:{\mathcal
Balanced_ternary
Mathematical function, denoted exp(x) or e^x
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 denoted e x
Exponential_function
Function used in signal processing
statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen
Window_function
Subfield of number theory
explicitly uses probability to answer questions about the integers and integer-valued functions. One basic idea underlying it is that different prime numbers
Probabilistic_number_theory
Function that is holomorphic on the whole complex plane
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane
Entire_function
Attribute of data
-> Bool denoting functions taking an integer and returning a Boolean. In C, a function is not a first-class data type but function pointers can be manipulated
Data_type
Indicator function of positive numbers
function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a step function named after Oliver Heaviside, the value
Heaviside_step_function
Computer programming language
basic types are integer, float, string, null, table, array, function, generator, class, instance, bool, thread and userdata. An Integer represents a 32
Squirrel (programming language)
Squirrel_(programming_language)
Logarithm of a complex number
k\right)} for integers k {\displaystyle k} . These logarithms are equally spaced along a vertical line in the complex plane. A complex-valued function log : U
Complex_logarithm
Mathematical concept
example, consider the real-valued function of a real variable given by f(x) = 5x − 7. One can think of f as the function which multiplies its input by
Inverse_function
Function that can be written as a sum over prime factors
an additive function is an arithmetic function f(n) of the positive integer variable n such that whenever a and b are coprime, the function applied to
Additive_function
Special mathematical function
of positive integer order arise in the calculation of processes represented by higher-order Feynman diagrams. The polylogarithm function is equivalent
Polylogarithm
Quantum mechanics principle
exclusion principle states that two or more identical particles with half-integer spins (i.e., fermions) cannot simultaneously occupy the same quantum state
Pauli_exclusion_principle
Open problem on 3x+1 and x/2 functions
positive integer: If the number is even, divide it by two. If the number is odd, triple it and add one. In modular arithmetic notation, define the function f
Collatz_conjecture
Number whose square is a given number
positional notation system. The square roots of small integers are used in both the SHA-1 and SHA-2 hash function designs to provide nothing up my sleeve numbers
Square_root
Solutions of Legendre's differential equation
called the degree and order of the relevant function, respectively. The polynomial solutions when λ is an integer (denoted n), and μ = 0 are the Legendre
Legendre_function
Largest integer that divides given integers
of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest
Greatest_common_divisor
Type of mathematical expression
addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of
Polynomial
real-valued functions defined on a topological space, as follows. The Baire class 0 functions are the continuous functions. The Baire class 1 functions are
Baire_function
Set of rules defining correctly structured programs
interpreted according to use. For example, ⌊3.2 gives 3, the largest integer not above the argument, and 3⌊2 gives 2, the lower of the two arguments
APL_syntax_and_symbols
Statistical method of dividing data into equal-sized intervals for analysis
a sample of size N by computing a real valued index h. When h is an integer, the h-th smallest of the N values, xh, is the quantile estimate. Otherwise
Quantile
Complex number whose mapping on a coordinate plane produces a triangular lattice
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the
Eisenstein_integer
Mathematical expression with disputed status
the exponent is of type integer; otherwise, it is considered as a transcendental function. ... If the exponent n is an integer, then exact operations are
Zero_to_the_power_of_zero
C function to format and output text
number of value arguments that the function serializes per the format string. Mismatch between the format specifiers and count and type of values results
Printf
Special functions of several complex variables
sum converges. This analytic function can be used to solve a combinatorics problem: in how many different ways can an integer be written as the sum of two
Theta_function
Rational number equal to an integer plus 1/2
{\pi ^{n/2}}{\Gamma ({\frac {n}{2}}+1)}}R^{n}~.} The values of the gamma function on half-integers are rational multiples of the square root of pi: Γ (
Half-integer
Number used for counting
2, 3, and so on, possibly excluding 0. The terms positive integers, non-negative integers, whole numbers, and counting numbers are also used. The set
Natural_number
Natural number
= 37 – 27 2060 – sum of the totient function for the first 82 integers 2061 – Number of sets of positive integers with arithmetic mean 7 2062 = ϕ ( ϕ
2000_(number)
Value for unrepresentable data
. The standard has alternative functions for powers: The standard pow function and the integer exponent pown function define 0 0 {\displaystyle 0^{0}}
NaN
INTEGER VALUED-FUNCTION
INTEGER VALUED-FUNCTION
Male
Welsh
Welsh name ALED means "offspring."
Female
Spanish
Spanish name SALUD means "health."
Surname or Lastname
English
English : topographic name for someone who lived in a valley, Middle English valeye.
Female
Swedish
Swedish contracted form of Scandinavian Ingegerd, INGER means "Ing's enclosure."
Girl/Female
Danish, Finnish, German, Swedish
Guarded by Ing; Ing's Beauty; Ing's Place
Boy/Male
English
Sage, wise. From the Old English Aelfraed, meaning elf counsel. Also from Ealdfrith or Alfrid,...
Boy/Male
Muslim
Newborn child.
Boy/Male
Muslim
To wait
Girl/Female
Biblical
The heap of witness.
Boy/Male
Anglo, British, English, Finnish, French, Swedish
Lives in the Valley; Valley; Usually with a Stream; Strong; Healthy
Girl/Female
British, English, Finnish, French, Latin
Valley; Usually with a Stream; Strong
Boy/Male
Muslim
Powerful, Patient
Male
English
Variant spelling of Middle English Alvred, ALURED means "elf counsel."
Boy/Male
English Latin
Strong.; the name of more than 50 saints and three Roman emperors.
Boy/Male
English
Lives in the valley.
Boy/Male
Arabic, Muslim
To Wait
Female
Scandinavian
Scandinavian form of Old Norse Ingigerðr, INGEGERD means "Ing's enclosure."
Boy/Male
Teutonic Swedish
Powerful ruler.
Male
Scandinavian
Scandinavian form of German Walther, VALTER means "ruler of the army."
Boy/Male
Anglo, British, English, Finnish, Swedish
Valley; Usually with a Stream; From the Glen
INTEGER VALUED-FUNCTION
INTEGER VALUED-FUNCTION
Girl/Female
Hindu
Nobel high, Sky, No limit
Boy/Male
Indian
Father of Pearl
Surname or Lastname
Irish (County Donegal)
Irish (County Donegal) : Anglicized form of Gaelic Ó Duibhidhir or sometimes of Mac Duibhidhir (see Dwyer, also Dyer).English : of uncertain derivation; possibly from diver, an agent derivative of Middle English dive ‘to dip or plunge’, but if so the application is obscure. It may be a nickname for someone compared to a diving bird. Compare Ducker.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Rama Krishna
Female
Slavic
Feminine form of Slavic Dragan, DRAGANA means "dear, beloved." In use by the Croatians and Serbians.
Surname or Lastname
English
English : habitational name from a minor place in the parish of Millom, Cumbria. The name is not recorded until the 13th century. The first element is probably from Middle English apostel ‘apostle’, used as a nickname or personal name (see Postle). Alternatively, it may represent a survival of an Old English personal name, Possel. The second element is northern Middle English thwaite ‘clearing’ (Old Norse þveit).
Boy/Male
Gujarati, Hindu, Indian, Sanskrit
Lord of Sky (Vyon); Very Special to World (Vyoni); Being Very Nature
Boy/Male
Hindu, Indian, Marathi, Mythological, Telugu
An Epithet of Lord Shiva
Female
Czechoslovakian
, love.
Girl/Female
Indian
Another name of holy Quran, Good news, Good omens
INTEGER VALUED-FUNCTION
INTEGER VALUED-FUNCTION
INTEGER VALUED-FUNCTION
INTEGER VALUED-FUNCTION
INTEGER VALUED-FUNCTION
v. t.
To raise to estimation; to cause to have value, either real or apparent; to enhance in value.
a.
Having a valve or valve; valvate.
a.
Consisting of, or having, three valves; opening with three valves; as, a three-valved pericarp.
n.
A complete entity; a whole number, in contradistinction to a fraction or a mixed number.
a.
Having inestimable value; invaluable.
v. t.
To rate highly; to have in high esteem; to hold in respect and estimation; to appreciate; to prize; as, to value one for his works or his virtues.
imp. & p. p.
of Value
n.
Value.
a.
Highly regarded; esteemed; prized; as, a valued contributor; a valued friend.
n.
The relative length or duration of a tone or note, answering to quantity in prosody; thus, a quarter note [/] has the value of two eighth notes [/].
v. t.
To deposit and cover in the earth; to bury; to inhume; as, to inter a dead body.
v. t.
To be worth; to be equal to in value.
a.
Having the form of a volume, or roil; as, volumed mist.
a.
Arched; concave; as, a vaulted roof.
v. t.
To estimate the value, or worth, of; to rate at a certain price; to appraise; to reckon with respect to number, power, importance, etc.
a.
Changed; altered; various; diversified; as, a varied experience; varied interests; varied scenery.
n.
In an artistical composition, the character of any one part in its relation to other parts and to the whole; -- often used in the plural; as, the values are well given, or well maintained.
n.
One who values; an appraiser.
a.
Not valued; not appraised; hence, not considered; disregarded; valueless; as, an unvalued estate.
n.
Precise signification; import; as, the value of a word; the value of a legal instrument