# Category: Exponentials

Derivative of the exponential map
In the theory of Lie groups, the exponential map is a map from the Lie algebra g of a Lie group G into G. In case G is a matrix Lie group, the exponential map reduces to the matrix exponential. The ex
List of integrals of hyperbolic functions
The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant a is assumed to
Exponential family
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, incl
Exponential decay
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is t
Exponential formula
In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the
Exponentiation
Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as "b (raised) to the (power of) n". When n is a positive integ
Index of logarithm articles
This is a list of logarithm topics, by Wikipedia page. See also the list of exponential topics. * Acoustic power * Antilogarithm * Apparent magnitude * Baker's theorem * Bel * Benford's law * B
Q-exponential
In combinatorial mathematics, a q-exponential is a q-analog of the exponential function,namely the eigenfunction of a q-derivative. There are many q-derivatives, for example, the classical q-derivativ
Van der Corput's method
In mathematics, van der Corput's method generates estimates for exponential sums. The method applies two processes, the van der Corput processes A and B which relate the sums into simpler sums which a
Decimal antilogarithm
No description available.
Four exponentials conjecture
In mathematics, specifically the field of transcendental number theory, the four exponentials conjecture is a conjecture which, given the right conditions on the exponents, would guarantee the transce
Exponential factorial
The exponential factorial is a positive integer n raised to the power of n − 1, which in turn is raised to the power of n − 2, and so on and so forth in a right-grouping manner. That is, The exponenti
Exponential minus 1
No description available.
Schanuel's conjecture
In mathematics, specifically transcendental number theory, Schanuel's conjecture is a conjecture made by Stephen Schanuel in the 1960s concerning the transcendence degree of certain field extensions o
Matrix exponential
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theo
Exponential integral
In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument.
Exponential sum
In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the functi
Exponential distribution
In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuo
Tetration
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though and the left-exponent xb are common. Under th
General antilogarithm
No description available.
Marshall–Olkin exponential distribution
In applied statistics, the Marshall–Olkin exponential distribution is any member of a certain family of continuous multivariate probability distributions with positive-valued components. It was introd
Six exponentials theorem
In mathematics, specifically transcendental number theory, the six exponentials theorem is a result that, given the right conditions on the exponents, guarantees the transcendence of at least one of a
Binary antilogarithm
No description available.
List of representations of e
The mathematical constant e can be represented in a variety of ways as a real number. Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two
Theory of fructification
In economics, the theory of fructification is a theory of the interest rate which was proposed by French economist and finance minister Anne Robert Jacques Turgot. The term theory of fructification is
Antilogarithm
No description available.
Growth curve (statistics)
The growth curve model in statistics is a specific multivariate linear model, also known as GMANOVA (Generalized Multivariate Analysis-Of-Variance). It generalizes MANOVA by allowing post-matrices, as
List of exponential topics
This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics. * Accelerating change * Approximating natural exponents (log base e) * Artin–Hasse exponential * Bacteri
Exponential function
The exponential function is a mathematical function denoted by or (where the argument x is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued functio
Soboleva modified hyperbolic tangent
The Soboleva modified hyperbolic tangent, also known as (parametric) Soboleva modified hyperbolic tangent activation function ([P]SMHTAF), is a special S-shaped function based on the hyperbolic tangen
Square (algebra)
In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a sup
Turán's method
In mathematics, Turán's method provides lower bounds for exponential sums and complex power sums. The method has been applied to problems in equidistribution. The method applies to sums of the form wh
Stretched exponential function
The stretched exponential function is obtained by inserting a fractional power law into the exponential function.In most applications, it is meaningful only for arguments t between 0 and +∞. With β =
Logarithmic spiral
A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called
Gudermannian function
In mathematics, the Gudermannian function relates a hyperbolic angle measure to a circular angle measure called the gudermannian of and denoted . The Gudermannian function reveals a close relationship
Gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form and with parametric extensionfor arbitrary real constants a, b and non-zero c. It is named a
In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number of multiplications. Using the form o
Infra-exponential
A growth rate is said to be infra-exponential or subexponential if it is dominated by all exponential growth rates, however great the doubling time. A continuous function with infra-exponential growth
Euler's identity
In mathematics, Euler's identity (also known as Euler's equation) is the equality where e is Euler's number, the base of natural logarithms,i is the imaginary unit, which by definition satisfies i2 =
Lindemann–Weierstrass theorem
In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: Lindemann–Weierstrass theorem
Wheat and chessboard problem
The wheat and chessboard problem (sometimes expressed in terms of rice grains) is a mathematical problem expressed in textual form as: If a chessboard were to have wheat placed upon each square such t
Double exponential function
A double exponential function is a constant raised to the power of an exponential function. The general formula is (where a>1 and b>1), which grows much more quickly than an exponential function. For
Base (exponentiation)
In exponentiation, the base is the number b in an expression of the form bn.
Baker–Campbell–Hausdorff formula
In mathematics, the Baker–Campbell–Hausdorff formula is the solution for to the equation for possibly noncommutative X and Y in the Lie algebra of a Lie group. There are various ways of writing the fo
Rule of 72
In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (u
Power law
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of
Catenary
In physics and geometry, a catenary (US: /ˈkætənɛri/, UK: /kəˈtiːnəri/) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform
Transseries
In mathematics, the field of logarithmic-exponential transseries is a non-Archimedean ordered differential field which extends comparability of asymptotic growth rates of elementary nontrigonometric f
List of integrals of exponential functions
The following is a list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals.
Common antilogarithm
No description available.
Pentation
In mathematics, pentation (or hyper-5) is the next hyperoperation after tetration and before hexation. It is defined as iterated (repeated) tetration, just as tetration is iterated exponentiation. It
Prime power
In mathematics, a prime power is a positive integer which is a power of a single prime number.For example: 7 = 71, 9 = 32 and 64 = 26 are prime powers, while6 = 2 × 3, 12 = 22 × 3 and 36 = 62 = 22 × 3
Natural exponential family
In probability and statistics, a natural exponential family (NEF) is a class of probability distributions that is a special case of an exponential family (EF).
In mathematics, particularly p-adic analysis, the p-adic exponential function is a p-adic analogue of the usual exponential function on the complex numbers. As in the complex case, it has an inverse f
Ordered exponential field
In mathematics, an ordered exponential field is an ordered field together with a function which generalises the idea of exponential functions on the ordered field of real numbers.
No description available.
Exponential tree
An exponential tree is almost identical to a binary search tree, with the exception that the dimension of the tree is not the same at all levels. In a normal binary search tree, each node has a dimens
Volatility tax
The volatility tax is a mathematical finance term, formalized by hedge fund manager Mark Spitznagel, describing the effect of large investment losses (or volatility) on compound returns. It has also b
Exponentiation by squaring
In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigrou
Proof that e is irrational
The number e was introduced by Jacob Bernoulli in 1683. More than half a century later, Euler, who had been a student of Jacob's younger brother Johann, proved that e is irrational; that is, that it c
Natural antilogarithm
No description available.