{{Short description, none
This is a list of exponential topics, by Wikipedia page. See also
list of logarithm topics.
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Accelerating change
In futures studies and the history of technology, accelerating change is the observed exponential nature of the rate of technological change in recent history, which may suggest faster and more profound change in the future and may or may not ...
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Approximating natural exponents (log base e)
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Artin–Hasse exponential
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Bacterial growth
250px, Growth is shown as ''L'' = log(numbers) where numbers is the number of colony forming units per ml, versus ''T'' (time.)
Bacterial growth is proliferation of bacterium into two daughter cells, in a process called binary fission. Providi ...
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Baker–Campbell–Hausdorff formula
In mathematics, the Baker–Campbell–Hausdorff formula gives the value of Z that solves the equation
e^X e^Y = e^Z
for possibly noncommutative and in the Lie algebra of a Lie group. There are various ways of writing the formula, but all ultima ...
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Cell growth
Cell most often refers to:
* Cell (biology), the functional basic unit of life
* Cellphone, a phone connected to a cellular network
* Clandestine cell, a penetration-resistant form of a secret or outlawed organization
* Electrochemical cell, a de ...
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Barometric formula
The barometric formula is a formula used to model how the air pressure (or air density) changes with altitude.
Pressure equations
There are two equations for computing pressure as a function of height. The first equation is applicable to the ...
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Beer–Lambert law
The Beer–Bouguer–Lambert (BBL) extinction law is an empirical relationship describing the attenuation in intensity of a radiation beam passing through a macroscopically homogenous medium with which it interacts. Formally, it states that the ...
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Characterizations of the exponential function
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Catenary
In physics and geometry, a catenary ( , ) is the curve that an idealized hanging chain or wire rope, cable assumes under its own weight when supported only at its ends in a uniform gravitational field.
The catenary curve has a U-like shape, ...
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Compound interest
Compound interest is interest accumulated from a principal sum and previously accumulated interest. It is the result of reinvesting or retaining interest that would otherwise be paid out, or of the accumulation of debts from a borrower.
Compo ...
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De Moivre's formula
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Derivative of the exponential map
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Doléans-Dade exponential
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Doubling time
The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things t ...
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''e''-folding
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Elimination half-life
Biological half-life (elimination half-life, pharmacological half-life) is the time taken for concentration of a biological substance (such as a medication) to decrease from its maximum concentration ( Cmax) to half of Cmax in the blood plasma. ...
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Error exponent
In information theory, the error exponent of a channel code or source code over the block length of the code is the rate at which the error probability decays exponentially with the block length of the code. Formally, it is defined as the limiti ...
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Euler's formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for ...
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Euler's identity
In mathematics, Euler's identity (also known as Euler's equation) is the Equality (mathematics), equality
e^ + 1 = 0
where
:e is E (mathematical constant), Euler's number, the base of natural logarithms,
:i is the imaginary unit, which by definit ...
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e (mathematical constant)
The number is a mathematical constant approximately equal to 2.71828 that is the base of a logarithm, base of the natural logarithm and exponential function. It is sometimes called Euler's number, after the Swiss mathematician Leonhard Eule ...
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Exponent
In mathematics, exponentiation, denoted , is an operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, i ...
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Exponent bias
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Exponential (disambiguation)
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Exponential backoff
Exponential backoff is an algorithm that uses feedback to multiplicatively decrease the rate of some process, in order to gradually find an acceptable rate. These algorithms find usage in a wide range of systems and processes, with radio networ ...
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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 is the quantity and (lambda
Lambda (; uppe ...
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Exponential dichotomy
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Exponential discounting
In economics, exponential discounting is a specific form of the discount function, used in the analysis of choice over time (with or without uncertainty). Formally, exponential discounting occurs when total utility is given by
U \Bigl(\_^ \Bigr ...
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Exponential diophantine equation
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Exponential dispersion model
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Exponential distribution
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuousl ...
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Exponential error
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Exponential factorial
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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, including the enabling of the user to calculate ...
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Exponential field
In mathematics, an exponential field is a Field (mathematics), field with a further unary operation that is a homomorphism from the field's additive group to its multiplicative group. This generalizes the usual idea of exponentiation on the real n ...
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Exponential formula
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Exponential function
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Exponential generating function
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Exponential-Golomb coding
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Exponential growth
Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present size. For example, when it is 3 times as big as it is now, it will be growing 3 times as fast ...
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Exponential hierarchy
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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.
Definitions
For real non-zero values of&nb ...
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Exponential integrator
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Exponential map (Lie theory)
In the theory of Lie groups, the exponential map is a map from the Lie algebra \mathfrak g of a Lie group G to the group, which allows one to recapture the local group structure from the Lie algebra. The existence of the exponential map is one o ...
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Exponential map (Riemannian geometry)
In Riemannian geometry, an exponential map is a map from a subset of a tangent space T''p'M'' of a Riemannian manifold (or pseudo-Riemannian manifold) ''M'' to ''M'' itself. The (pseudo) Riemannian metric determines a canonical affine connec ...
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Exponential map (discrete dynamical systems)
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Exponential notation
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Exponential object
In mathematics, specifically in category theory, an exponential object or map object is the category theory, categorical generalization of a function space in set theory. Category (mathematics), Categories with all Product (category theory), fini ...
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category theory
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory ...
)
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Exponential polynomials—see also
Touchard polynomials
The Touchard polynomials, studied by , also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by
:T_n(x)=\sum_^n S(n,k)x^k=\sum_^n
\left\x^k,
where S(n,k)=\left\ is a Stirling ...
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combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
)
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Exponential response formula
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Exponential sheaf sequence
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Exponential smoothing
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponen ...
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Exponential stability
In control theory, a continuous linear time-invariant system (LTI) is exponentially stable if and only if the system has eigenvalues (i.e., the poles of input-to-output systems) with strictly negative real parts (i.e., in the left half of the c ...
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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 function
:e(x) = \exp(2\pi ix).\,
Therefore, a typi ...
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Exponential time
In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations p ...
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Sub-exponential time
In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations p ...
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Exponential tree
An exponential tree is a type of search tree
In computer science, a search tree is a tree data structure used for locating specific keys from within a set. In order for a tree to function as a search tree, the key for each node must be greate ...
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Exponential type
In complex analysis, a branch of mathematics, a holomorphic function is said to be of exponential type C if its growth is bounded by the exponential function e^ for some real-valued constant C as , z, \to\infty. When a function is bounded in ...
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Exponentially equivalent measures
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Exponentiating by squaring
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Exponentiation
In mathematics, exponentiation, denoted , is an operation (mathematics), operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication ...
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Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive number, positive integers , , and satisfy the equation for any integer value of greater than . The cases ...
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Forgetting curve
The forgetting curve hypothesizes the decline of memory retention in time. This curve shows how information is lost over time when there is no attempt to retain it. A related concept is the strength of memory that refers to the durability that m ...
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Gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function (mathematics), function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real number, rea ...
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Gudermannian function
In mathematics, the Gudermannian function relates a hyperbolic angle measure \psi to a circular angle measure \phi called the ''gudermannian'' of \psi and denoted \operatorname\psi. The Gudermannian function reveals a close relationship betwe ...
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Half-exponential function
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Half-life Half-life is a mathematical and scientific description of exponential or gradual decay.
Half-life, half life or halflife may also refer to:
Film
* Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang
* ''Half Life: ...
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Hyperbolic function
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the ...
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Inflation
In economics, inflation is an increase in the average price of goods and services in terms of money. This increase is measured using a price index, typically a consumer price index (CPI). When the general price level rises, each unit of curre ...
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inflation rate
In economics, inflation is an increase in the average price of goods and services in terms of money. This increase is measured using a price index, typically a consumer price index (CPI). When the general price level rises, each unit of curre ...
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Interest
In finance and economics, interest is payment from a debtor or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct f ...
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Lambert W function
In mathematics, the Lambert function, also called the omega function or product logarithm, is a multivalued function, namely the Branch point, branches of the converse relation of the function , where is any complex number and is the expone ...
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Lifetime (physics)
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Limiting factor
A limiting factor is a variable of a system that causes a noticeable change in output or another measure of a type of system. The limiting factor is in a pyramid shape of organisms going up from the producers to consumers and so on. A factor not l ...
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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:
In other words, the extension field \mathbb(e^, \dots, e^) has transc ...
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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.
Indefinite integral
Indefinite integrals are antiderivative functions. A constant (the constant of integ ...
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List of integrals of hyperbolic functions
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Lyapunov exponent
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Malthusian catastrophe
Malthusianism is a theory that population growth is potentially exponential, according to the Malthusian growth model, while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of tr ...
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Malthusian growth model
A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert ...
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Marshall–Olkin exponential distribution
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Matrix exponential
In mathematics, the matrix exponential is a matrix function on square matrix, square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exp ...
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Moore's law
Moore's law is the observation that the Transistor count, number of transistors in an integrated circuit (IC) doubles about every two years. Moore's law is an observation and Forecasting, projection of a historical trend. Rather than a law of ...
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Nachbin's theorem
In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is a result used to establish bounds on the growth rates for analytic functions. In particular, Nachbin's theorem may be used to give the domain o ...
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Piano key frequencies
This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (refe ...
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p-adic exponential function
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Power law
In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a relative change in the other quantity proportional to the ...
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Proof that e is irrational
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Proof that e is transcendental
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Q-exponential
The term ''q''-exponential occurs in two contexts. The q-exponential distribution, based on the Tsallis q-exponential is discussed in elsewhere.
In combinatorial mathematics, a ''q''-exponential is a ''q''-analog of the exponential function, ...
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Radioactive decay
Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is conside ...
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Rule of 70,
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 (usually years) to obtain the approximate number ...
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Scientific notation
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to as scientif ...
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Six exponentials theorem
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Spontaneous emission
Spontaneous emission is the process in which a Quantum mechanics, quantum mechanical system (such as a molecule, an atom or a subatomic particle) transits from an excited state, excited energy state to a lower energy state (e.g., its ground state ...
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Super-exponentiation
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Tetration
In mathematics, tetration (or hyper-4) is an operation (mathematics), operation based on iterated, or repeated, exponentiation. There is no standard mathematical notation, notation for tetration, though Knuth's up arrow notation \uparrow \upa ...
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Versor
In mathematics, a versor is a quaternion of Quaternion#Norm, norm one, also known as a unit quaternion. Each versor has the form
:u = \exp(a\mathbf) = \cos a + \mathbf \sin a, \quad \mathbf^2 = -1, \quad a \in ,\pi
where the r2 = −1 conditi ...
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Weber–Fechner law
The Weber–Fechner laws are two related scientific law, scientific laws in the field of psychophysics, known as Weber's law and Fechner's law. Both relate to human perception, more specifically the relation between the actual change in a physica ...
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Wilkie's theorem
In mathematics, Wilkie's theorem is a result by Alex Wilkie about the theory of ordered fields with an exponential function, or equivalently about the geometric nature of exponential varieties.
Formulations
In terms of model theory, Wilkie's the ...
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Zenzizenzizenzic Zenzizenzizenzic is an obsolete form of mathematical notation representing the eighth power of a number (that is, the zenzizenzizenzic of ''x'' is ''x''8), dating from a time when powers were written out in words rather than as superscript numbers. ...
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Exponentials
Exponential may refer to any of several mathematical topics related to exponentiation, including:
*Exponential function, also:
**Matrix exponential, the matrix analogue to the above
*Exponential decay, decrease at a rate proportional to value
*Expo ...
Exponential
Exponential may refer to any of several mathematical topics related to exponentiation, including:
* Exponential function, also:
**Matrix exponential, the matrix analogue to the above
*Exponential decay, decrease at a rate proportional to value
* Ex ...