Characterizations of the exponential function information

In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article...

The exponential function is a mathematical function denoted by f ( x ) = exp ⁡ ( x ) {\displaystyle f(x)=\exp(x)} or e x {\displaystyle e^{x}} (where...

Artin–Hasse exponential Bacterial growth Baker–Campbell–Hausdorff formula Cell growth Barometric formula Beer–Lambert law Characterizations of the exponential function...

The stretched exponential function f β ( t ) = e − t β {\displaystyle f_{\beta }(t)=e^{-t^{\beta }}} is obtained by inserting a fractional power law into...

not a root of any polynomial with rational coefficients, as is eα for any non-zero algebraic α. Characterizations of the exponential function Transcendental...

Characterizations of the exponential function). If the observed value of X is 100, then the estimate is 1, although the true value of the quantity being...

\zeta >0} Characterizations of the exponential function Exponential growth Exponentiation Generalised logistic function Logistic distribution...

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...

and to define the Weierstrass transform. Gaussian functions arise by composing the exponential function with a concave quadratic function: f ( x ) = exp...

1/Γ(z) is an entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential function: Γ ( z ) = M { e − x...

shifted exponential with the weight being a function of the normal distribution. The probability density function (pdf) of the exponentially modified...

K_{x}}} where the limit definition of the exponential has been used (see also characterizations of the exponential function). More generally B (...

Maclaurin series. The exponential function is analytic. Any Taylor series for this function converges not only for x close enough to x0 (as in the definition)...

number), a quadratic function c x 2 {\displaystyle cx^{2}} ( c {\displaystyle c} as a nonnegative real number) and an exponential function c e x {\displaystyle...

sets is the exponential of the exponential generating function for connected structures. The exponential formula is a power series version of a special...

exponential polynomials are functions on fields, rings, or abelian groups that take the form of polynomials in a variable and an exponential function...

multi-valued function. For example, the complex logarithm is the multi-valued inverse of the complex exponential function. Similarly, the discrete logarithm...

exactly an exponential distribution scaled by 1/2. The probability density function of the Laplace distribution is also reminiscent of the normal distribution;...

and statistics, the gamma distribution is a versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang...

{\displaystyle h} is an example of a function that is differentiable but not locally Lipschitz continuous. The exponential function e x {\displaystyle e^{x}}...

For example, addition and division, the factorial and exponential function, and the function which returns the nth prime are all primitive recursive...

will present some of the "characterizations" of the notion of "algorithm" in more detail. Over the last 200 years, the definition of the algorithm has become...

In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input...

geometric distributions of non-negative integers and the exponential distributions of non-negative real numbers. In the context of Markov processes, memorylessness...