Physical world and mathematics

Exponential function

The exponential function, also called the natural exponential function, is the mathematical function exp(x) = e^x, with e ≈ 2.718; it is its own derivative and models growth and decay.

Exponential generating functions

An exponential generating function (EGF) attaches to a counting sequence the power series sum a_n x^n/n!, the standard tool of enumerative combinatorics for labeled structures like permutations and set partitions.

Exponential growth

Exponential growth, also called geometric growth, is increase at a rate proportional to the current value, giving a constant doubling time; it models populations, epidemics, and compound interest.

Exponential integral

The exponential integral, or Ei function, is a special function defined by the integral of e−t/t, introduced by Legendre in 1811 and arising throughout physics and engineering.

Exponential integrator

An exponential integrator is a time-stepping method for stiff or oscillatory semilinear differential equations that solves the linear part exactly through a matrix exponential, dating to the 1960s.

Exponential map (Riemannian geometry)

The exponential map of a Riemannian manifold sends a tangent vector at a point to the endpoint of the geodesic starting there, and underlies normal coordinates and geodesic completeness.

Exponential smoothing

Exponential smoothing, also known as Holt-Winters, is a family of time series forecasting methods that weight recent observations more heavily, proposed in the late 1950s.

Exponential stability

Exponential stability is a strong form of stability of an equilibrium point of a dynamical system: nearby solutions converge to it at least as fast as a decaying exponential.

Exponential sum

An exponential sum, also called a trigonometric sum, is a finite sum of complex roots of unity, central to analytic number theory since Gauss's 1801 work.

Exponential time differencing

Exponential time differencing (ETD) is a family of numerical methods for stiff semilinear differential equations that integrates the linear part exactly with matrix exponentials, dating to the 1960s.

Exponential time hypothesis

The exponential time hypothesis (ETH) is an unproven conjecture in computational complexity theory, proposed by Impagliazzo and Paturi in 2001, stating that 3-SAT cannot be decided in subexponential time.

Exponentiation

Exponentiation is the arithmetic operation that raises a base to an exponent, written as a superscript; for positive integer exponents it means repeated multiplication, extending to zero, negative, rational, real, and complex exponents.

Exponentiation by squaring

Exponentiation by squaring, also called binary exponentiation or the square-and-multiply algorithm, computes large powers using multiplications proportional to the logarithm of the exponent, making modular exponentiation in RSA practical.

Export production

Export production (EP) is the organic carbon produced in the ocean's sunlit surface layer that sinks toward the deep ocean, linking photosynthesis to the biological carbon pump.

Oct 22, 2026

EXPRES

EXPRES, the EXtreme PREcision Spectrograph, is an echelle spectrograph built at Yale and installed on the 4.3-meter Lowell Discovery Telescope in Arizona to detect Earth-like exoplanets.

Expressed protein ligation

Expressed protein ligation (EPL) is a protein semisynthesis method that chemically joins a recombinant protein fragment to a synthetic peptide; it was first reported in 1998.

Expression (mathematics)

In mathematics, an expression is a finite combination of numbers, variables, and operation symbols standing for a calculation, and an equation joins two expressions with an equal sign.

Ext functor

The Ext functor, or Ext group, is a family of functors in homological algebra defined as the right derived functors of the Hom functor, named for extensions.

Extended Chandra Deep Field South

The Extended Chandra Deep Field-South (E-CDF-S) is a Chandra X-ray survey of about 0.3 square degrees flanking the original Chandra Deep Field-South, made with four deep pointings.

Extended Euclidean algorithm

The extended Euclidean algorithm, also called extended GCD, computes the greatest common divisor of two integers plus Bézout coefficients, and is used to find modular inverses in cryptography.

Extended finite element method

The extended finite element method (XFEM) is a numerical technique of computational mechanics, reported by Moës, Dolbow, and Belytschko in 1999, that models cracks and interfaces without remeshing.

Extended Groth Strip

The Extended Groth Strip is a narrow strip of sky in Ursa Major containing at least 50,000 galaxies, one of the most intensively studied extragalactic fields.

Extended Hubbard model

The extended Hubbard model, often called the U-V model at low density, adds intersite Coulomb repulsion between neighboring sites to the standard Hubbard model, stabilizing charge-ordered states.

Extended Kalman filter

The extended Kalman filter (EKF) is a state-estimation algorithm applying the Kalman filter to nonlinear systems by linearizing about the current estimate, developed at NASA Ames in the early 1960s for Apollo lunar navigation.

Extended periodic table

The extended periodic table is the theoretical extension of the periodic table beyond oganesson, element 118, into a hypothetical eighth period beginning with element 119.

Extended precision

Extended precision is an IEEE 754 floating-point format exceeding its associated basic format in precision and range, in practice usually Intel's x87 80-bit format with 64 significant bits.

Extended X-ray absorption fine structure spectroscopy

Extended X-ray absorption fine structure (EXAFS) spectroscopy is an element-specific X-ray technique that determines which neighbors surround an element, at what distances and numbers, probing local structure within about 5 Å without requiring long-range crystalline order.