as ln(x) or loge(x). Legendre's constant is a mathematical constant occurring in a formula constructed by Adrien-Marie Legendre to approximate the behavior...

Landau–Ramanujan constant – Edmund Landau and Srinivasa Ramanujan Legendre's constant (one, 1) – Adrien-Marie Legendre Loschmidt constant – Johann Josef...

Adrien-Marie Legendre Associated Legendre polynomials Gauss–Legendre algorithm Legendre's constant Legendre's equation in number theory Legendre's functional...

depending on the application. 1 is the value of Legendre's constant, introduced in 1808 by Adrien-Marie Legendre to express the asymptotic behavior of the prime-counting...

the polynomials were first defined by Legendre in 1782. A third definition is in terms of solutions to Legendre's differential equation: This differential...

In probability theory, a normalizing constant or normalizing factor is used to reduce any probability function to a probability density function with total...

The number π (/paɪ/ ; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its...

Prime-counting function Meissel–Lehmer algorithm Offset logarithmic integral Legendre's constant Skewes' number Bertrand's postulate Proof of Bertrand's postulate...

condition Legendre–Fenchel transformation Legendre's conjecture Legendre's constant Legendre's differential equation Legendre's equation Legendre's formula...

real line, the Legendre transform f ∗ {\displaystyle f^{*}} of a function f {\displaystyle f} can be specified, up to an additive constant, by the condition...

possible to find a different constant A that will work with this middle exponent to always produce primes. Moreover, if Legendre's conjecture is true, the...

In mathematics, Apéry's constant is the infinite sum of the reciprocals of the positive integers, cubed. That is, it is defined as the number ζ ( 3 ) =...

In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation ( 1 − x 2 ) d 2 d x 2 P ℓ m ( x ) − 2...

of the factorial function to the gamma function. Adrien-Marie Legendre included Legendre's formula, describing the exponents in the factorization of factorials...

{1}{2}}})={\tfrac {1}{2}}\pi } The Legendre's relation for tangential modular counterparts results directly from the Legendre's identity for Pythagorean modular...

root of two is occasionally called Pythagoras's number or Pythagoras's constant. In ancient Roman architecture, Vitruvius describes the use of the square...

Hirschhorn gives a short proof derived from the Jacobi triple product. Legendre's three-square theorem Lagrange's four-square theorem Sum of squares function...

Lucas. Like every sequence defined by a homogeneous linear recurrence with constant coefficients, the Fibonacci numbers have a closed-form expression. It has...

instead use z!). Legendre's normalization does simplify some formulae, but complicates others. From a modern point of view, the Legendre normalization of...

conjecture: Are there infinitely many primes p such that p + 2 is prime? Legendre's conjecture: Does there always exist at least one prime between consecutive...

Constant k filters, also k-type filters, are a type of electronic filter designed using the image method. They are the original and simplest filters produced...

_{0}^{2})}}}{\ s^{2}+\omega _{\mathrm {f} }^{2}\ }}\ \right]} Isolating the constant and using equivalent fractions to adjust for lack of numerator:   ω 0 2...

centre, Rubin and collaborators found instead that they remain almost constant – the rotation curves are said to be "flat". This observation necessitates...

logarithm of infinity!); Legendre's argument is heuristic; and Chebyshev's proof, although perfectly sound, makes use of the Legendre-Gauss conjecture, which...

integrals (considered as solutions of a differential equation) is a constant. Legendre's relation stated using elliptic functions is ω 2 η 1 − ω 1 η 2 = 2...

polynomials of degree 2n − 1 or less. This exact rule is known as the Gauss–Legendre quadrature rule. The quadrature rule will only be an accurate approximation...

inappropriate behavior toward underage female students at the time, paying them constant attention, and even showing up at a party where young people were drinking...

same data as Laplace for the shape of the Earth. Within ten years after Legendre's publication, the method of least squares had been adopted as a standard...

mathematician and number theorist. In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which...

y'+\lambda \,y=0\qquad {\text{with}}\qquad \lambda =n(n+1).} This is Legendre's equation. The second form of the differential equation is: d d x [ ( 1...