Friedrich Gauss, the integral is ∫ − ∞ ∞ e − x 2 d x = π . {\displaystyle \int _{-\infty }^{\infty }e^{-x^{2}}\,dx={\sqrt {\pi }}.} Abraham de Moivre originally...

physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations...

the Wald distribution Gauss code – described on website of University of Toronto Gauss linking integral (knot theory) Gauss's algorithm for determination...

Johann Carl Friedrich Gauss (German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs] ; Latin: Carolus Fridericus Gauss; 30 April 1777 – 23 February 1855) was a German mathematician...

Friedrich Gauss. It states that the flux (surface integral) of the gravitational field over any closed surface is proportional to the mass enclosed. Gauss's law...

mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that the...

Euler, but the first full systematic treatment was given by Carl Friedrich Gauss (1813). Studies in the nineteenth century included those of Ernst Kummer (1836)...

modified, as elaborated below.) Gauss's law for magnetism can be written in two forms, a differential form and an integral form. These forms are equivalent...

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field...

them in the 1960s, and Carl Friedrich Gauss. The problem in numerical integration is to approximate definite integrals of the form ∫ a b f ( x ) d x . {\displaystyle...

denotes the double factorial. In terms of the Gauss hypergeometric function, the complete elliptic integral of the first kind can be expressed as K ( k...

quadrature rules, such as Gauss-Hermite quadrature for integrals on the whole real line and Gauss-Laguerre quadrature for integrals on the positive reals...

setup Schwarz integral formula Parseval–Gutzmer formula Bochner–Martinelli formula Helffer–Sjöstrand formula Titchmarsh 1939, p. 84 "Gauss's Mean-Value Theorem"...

formulation of Gauss equation up to a trivial rearrangement. Similarly rewriting the magnetic flux in Gauss's law for magnetism in integral form gives ∮...

Curve Fenchel's theorem Theorema egregium Gauss–Bonnet theorem First fundamental form Second fundamental form Gauss–Codazzi–Mainardi equations Dupin indicatrix...

polynomials Gauss–Legendre algorithm Legendre's constant Legendre's equation in number theory Legendre's functional relation for elliptic integrals Legendre's...

the German school of mathematical thinking, under which Carl Friedrich Gauss and his followers largely determined the lines on which mathematics developed...

to have considered the factorial of a complex number, as instead Gauss first did. Gauss also proved the multiplication theorem of the gamma function and...

theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial with...

constant have been calculated. Gauss's constant, denoted by G, is equal to ϖ /π ≈ 0.8346268 and named after Carl Friedrich Gauss, who calculated it via the...

us mention two classical examples, Dirichlet’s divisor problem and the Gauss’ circle problem. The former estimates the size of d(n), the number of positive...

is positive then the digamma function has the following integral representation due to Gauss: ψ ( z ) = ∫ 0 ∞ ( e − t t − e − z t 1 − e − t ) d t . {\displaystyle...

of integrals on algebraic manifolds: Summary of main results and discussion of open problems (Gives a quick sketch of main structure theorem of Gauss–Manin...

as a rotation. The complex plane is sometimes called the Argand plane or Gauss plane. In complex analysis, the complex numbers are customarily represented...

if the charge is in motion). Outline of proof Taking S in the integral form of Gauss's law to be a spherical surface of radius r, centered at the point...

The shoelace formula, also known as Gauss's area formula and the surveyor's formula, is a mathematical algorithm to determine the area of a simple polygon...

In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. The word...

considering a Gaussian surface around a body. Mathematically, Gauss's law takes the form of an integral equation: Φ E = ∮ S E ⋅ d A = Q enclosed ε 0 = ∫ V ρ ε...

approximating function, the logarithmic integral li(x) (under the slightly different form of a series, which he communicated to Gauss). Both Legendre's and Dirichlet's...

integral of the curvature over the whole surface. As a special case of what is now called the Gauss–Bonnet theorem, Gauss proved that this integral was...