In number theory, a normal order of an arithmetic function is some simpler or better-understood function which "usually" takes the same or closely approximate...

In number theory, an average order of an arithmetic function is some simpler or better-understood function which takes the same values "on average". Let...

In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose domain is the set of positive integers and...

with its Hermitian adjoint Normal order of an arithmetic function, a type of asymptotic behavior useful in number theory Normal polytopes, in polyhedral...

axiomatic set theory, a function f : Ord → Ord is called normal (or a normal function) if it is continuous (with respect to the order topology) and strictly...

computer science Normal order of an arithmetic function in number theory Normal (disambiguation) Regular (disambiguation) Regular order (disambiguation)...

number theory. It is useful for proving results about the normal order of an arithmetic function.: 305–308  The theorem was proved in a special case in 1934...

extremal orders of an arithmetic function are best possible bounds of the given arithmetic function. Specifically, if f(n) is an arithmetic function and m(n)...

statistics, the arithmetic mean ( /ˌærɪθˈmɛtɪk/ arr-ith-MET-ik), arithmetic average, or just the mean or average is the sum of a collection of numbers divided...

law that rationalizes the choice of arithmetic mean as an estimator of the location parameter, is the normal law of errors: φ Δ = h √ π e − h h Δ Δ , {\displaystyle...

X has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution...

foundation of first-order logic. A theory about a topic, such as set theory, a theory for groups, or a formal theory of arithmetic, is usually a first-order logic...

degree of a function is the order of the highest order monomial in its algebraic normal form Circuit complexity attempts to classify Boolean functions with...

In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation...

hierarchy assigns classifications to the formulas in the language of first-order arithmetic. The classifications are denoted Σ n 0 {\displaystyle \Sigma _{n}^{0}}...

far-call instruction to start the interrupt-function manually after pushing the flag register. An example of a useful DOS software interrupt was interrupt...

computing function bounds. Numerical methods involving interval arithmetic can guarantee relatively reliable and mathematically correct results. Instead of representing...

quasi-arithmetic mean or generalised f-mean or Kolmogorov-Nagumo-de Finetti mean is one generalisation of the more familiar means such as the arithmetic mean...

standard, the right shift of a negative number is implementation defined. Most implementations, e.g., the GCC, use an arithmetic shift (i.e., sign extension)...

statement that cannot be proved in ATR0 (a second-order arithmetic theory with a form of arithmetical transfinite recursion). In 2004, the result was generalized...

of much of Principia Mathematica, now known as first-order logic, is complete, Peano arithmetic is necessarily incomplete if it is consistent. This is...

Lamé function Mathieu function Mittag-Leffler function Painlevé transcendents Parabolic cylinder function Arithmetic–geometric mean Ackermann function: in...

geometric means. The arithmetic–geometric mean is used in fast algorithms for exponential, trigonometric functions, and other special functions, as well as some...

In mathematics, the Veblen functions are a hierarchy of normal functions (continuous strictly increasing functions from ordinals to ordinals), introduced...

floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a significand (a signed sequence of a fixed number of digits in some...

represents N−1(F(x)), where N−1(.) represents the inverse cumulative normal distribution function. The points plotted in a Q–Q plot are always non-decreasing when...

theory of first-order Peano arithmetic seems consistent. Assuming this is indeed the case, note that it has an infinite but recursively enumerable set of axioms...

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...

In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers...

numbers is the arithmetic mean – the sum of the numbers divided by how many numbers are in the list. For example, the mean or average of the numbers 2...