{{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 be ...
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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. Providing ...
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Baker–Campbell–Hausdorff formula
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Cell growth
Cell growth refers to an increase in the total mass of a cell, including both cytoplasmic, nuclear and organelle volume. Cell growth occurs when the overall rate of cellular biosynthesis (production of biomolecules or anabolism) is greater th ...
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Barometric formula
The barometric formula, sometimes called the '' exponential atmosphere'' or ''isothermal atmosphere'', is a formula used to model how the pressure (or density) of the air changes with altitude. The pressure drops approximately by 11.3 pascals per ...
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Beer–Lambert law
The Beer–Lambert law, also known as Beer's law, the Lambert–Beer law, or the Beer–Lambert–Bouguer law relates the attenuation of light to the properties of the material through which the light is travelling. The law is commonly applied t ...
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Characterizations of the exponential function In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent o ...
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Catenary
In physics and geometry, a catenary (, ) is the curve that an idealized hanging chain or 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, superfici ...
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Compound interest
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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 ...
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''e''-folding
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Elimination half-life
Biological half-life (also known as elimination half-life, pharmacologic 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 b ...
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Error exponent
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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 ...
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Euler's identity
In mathematics, Euler's identity (also known as Euler's equation) is the equality
e^ + 1 = 0
where
: is Euler's number, the base of natural logarithms,
: is the imaginary unit, which by definition satisfies , and
: is pi, the ratio of the circ ...
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e (mathematical constant)
The number , also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of the natural logarithms. It is the limit of as approaches infinity, an expressi ...
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Exponent
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to r ...
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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 network ...
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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) is a positive rate ...
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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(\_^)=\sum_^\de ...
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Exponential diophantine equation
In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a ...
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Exponential dispersion model
In probability and statistics, the class of exponential dispersion models (EDM) is a set of probability distributions that represents a generalisation of the natural exponential family.Jørgensen, B. (1987). Exponential dispersion models (with dis ...
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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 continuously and independently at a constant average ...
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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
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Exponential formula
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Exponential function
The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, ...
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Exponential generating function
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Exponential-Golomb coding
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Exponential growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a ...
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Exponential hierarchy In computational complexity theory, the exponential hierarchy is a hierarchy of complexity classes, which is an exponential time analogue of the polynomial hierarchy. As elsewhere in complexity theory, “exponential” is used in two different me ...
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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 ...
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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 of ...
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Exponential map (Riemannian geometry)
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Exponential map (discrete dynamical systems)
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Exponential notation
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Exponential object (
category theory
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, ca ...
)
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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 numbe ...
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combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...
)
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Exponential response formula
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Exponential sheaf sequence In mathematics, the exponential sheaf sequence is a fundamental short exact sequence of sheaves used in complex geometry.
Let ''M'' be a complex manifold, and write ''O'M'' for the sheaf of holomorphic functions on ''M''. Let ''O'M''* be th ...
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Exponential smoothing
Exponential smoothing 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, exponential functions are used to assign expo ...
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Exponential stability
:''See Lyapunov stability, which gives a definition of asymptotic stability for more general dynamical systems. All exponentially stable systems are also asymptotically stable.''
In control theory, a continuous linear time-invariant system (LTI) ...
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Exponential sum
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Exponential time
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Sub-exponential time
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Exponential tree
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Exponential type
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Exponentially equivalent measures
In mathematics, exponential equivalence of measures is how two sequences or families of probability measures are "the same" from the point of view of large deviations theory.
Definition
Let (M,d) be a metric space and consider two one-parameter f ...
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Exponentiating by squaring
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Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to ...
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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 integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been ...
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Forgetting curve
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Gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real constants , and non-zero . It is ...
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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 (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ...
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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 u ...
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Inflation
In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduct ...
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inflation rate
In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reductio ...
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Interest
In finance and economics, interest is payment from a borrower 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 distin ...
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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 transce ...
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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 inte ...
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List of integrals of hyperbolic functions
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Lyapunov exponent
In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectory, trajectories. Quantitatively, two trajectories in phase sp ...
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Malthusian catastrophe
Malthusianism is the idea that population growth is potentially exponential while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of triggering a population die off. This event, c ...
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Malthusian growth model
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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 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 exponential give ...
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Moore's law
Moore's law is the observation that the number of transistors in a dense integrated circuit (IC) doubles about every two years. Moore's law is an observation and projection of a historical trend. Rather than a law of physics, it is an empi ...
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Nachbin's theorem
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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 functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one q ...
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Proof that e is irrational
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Proof that e is transcendental
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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''-derivative, the Askey-Wilson ...
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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 consid ...
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Rule of 70,
Rule of 72
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Scientific notation
Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, o ...
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Six exponentials theorem
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Spontaneous emission
Spontaneous emission is the process in which a quantum mechanical system (such as a molecule, an atom or a subatomic particle) transits from an excited energy state to a lower energy state (e.g., its ground state) and emits a quantized amount ...
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Super-exponentiation
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Tetration
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though \uparrow \uparrow and the left-exponent ''xb'' are common.
Under the definition as rep ...
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Versor
In mathematics, a versor is a quaternion of norm one (a ''unit quaternion''). The word is derived from Latin ''versare'' = "to turn" with the suffix ''-or'' forming a noun from the verb (i.e. ''versor'' = "the turner"). It was introduced by Will ...
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Wilkie's theorem
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Zenzizenzizenzic
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Exponentials
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
*Expo ...