In mathematics, the Euler sequence is a particular exact sequence of sheaves on n-dimensional projective space over a ring. It shows that the sheaf of...

In mathematics, the Euler numbers are a sequence En of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion 1 cosh ⁡ t = 2 e...

(single or sequence), or other mathematical entity. Many of these entities have been given simple yet ambiguous names such as Euler's function, Euler's equation...

algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant...

kinds of sequences are called "Euler angles". In that case, the sequences of the first group are called proper or classic Euler angles. The Euler angles...

503, 547, 593, 641, 691, 743, 797, 853, 911, 971, ... (sequence A005846 in the OEIS). Euler's lucky numbers are unrelated to the "lucky numbers" defined...

Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions. This article explains how to convert between the...

sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant,...

Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known...

In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the...

An Euler diagram (/ˈɔɪlər/, OY-lər) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining...

logarithm, also commonly written as ln(x) or loge(x). Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually...

(ed.). "Sequence A245886 (Decimal expansion of Gamma(-3/2), where Gamma is Euler's gamma function)". The On-Line Encyclopedia of Integer Sequences. OEIS...

In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum. It can be used to approximate...

numerical analysis and scientific computing, the backward Euler method (or implicit Euler method) is one of the most basic numerical methods for the...

In mathematics, an exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian...

posthumously in 1873 by Carl Hierholzer. This is known as Euler's Theorem: A connected graph has an Euler cycle if and only if every vertex has an even number...

In mathematics, an odd composite integer n is called an Euler pseudoprime to base a, if a and n are coprime, and a ( n − 1 ) / 2 ≡ ± 1 ( mod n ) {\displaystyle...

transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences. It is closely related to the Euler transform...

the case m = n − 1. Euler's rule creates additional amicable pairs for (m,n) = (1,8), (29,40) with no others being known. Euler (1747 & 1750) overall...

coefficients. They are used for series expansion of functions, and with the Euler–MacLaurin formula. These polynomials occur in the study of many special...

from Milnor−Stasheff, but seems more natural. The sequence is sometimes called the Euler sequence. Hartshorne, Ch. II. Theorem 8.13. In a ring-theoretic...

certain vertical and diagonal lines, and amongst these the so-called Euler sequences with high concentrations of primes are discovered." Diagonal, horizontal...

Appell sequences besides the trivial example { x n } {\displaystyle \{x^{n}\}} are the Hermite polynomials, the Bernoulli polynomials, and the Euler polynomials...

the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII), in which he proposed the following conjecture: dass jede...

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...

In mathematics, the Euler function is given by ϕ ( q ) = ∏ k = 1 ∞ ( 1 − q k ) , | q | < 1. {\displaystyle \phi (q)=\prod _{k=1}^{\infty }(1-q^{k}),\quad...

{\displaystyle {\mathcal {O}}(1)} . Namely, there is a short exact sequence, the Euler sequence: 0 → O P n → O ( 1 ) ⊕ n + 1 → T P n → 0. {\displaystyle 0\to...

Euler first pointed out that the choice of route inside each land mass is irrelevant and that the only important feature of a route is the sequence of...

is nowadays one of the cornerstones of algebraic geometry. Euler sequence The exact sequence of sheaves: 0 → O P n → O P n ( 1 ) ⊕ ( n + 1 ) → T P n →...