In mathematics, the Bernoulli numbers Bn are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can...

2024. Bernoulli differential equation Bernoulli distribution Bernoulli number Bernoulli polynomials Bernoulli process Bernoulli trial Bernoulli's principle...

Jacob Bernoulli (also known as James in English or Jacques in French; 6 January 1655 [O.S. 27 December 1654] – 16 August 1705) was one of the many prominent...

Daniel Bernoulli FRS (/bɜːrˈnuːli/ bur-NOO-lee; Swiss Standard German: [ˈdaːni̯eːl bɛrˈnʊli]; 8 February [O.S. 29 January] 1700 – 27 March 1782) was a...

In mathematics, poly-Bernoulli numbers, denoted as B n ( k ) {\displaystyle B_{n}^{(k)}} , were defined by M. Kaneko as L i k ( 1 − e − x ) 1 − e − x...

Johann Bernoulli (also known as Jean in French or John in English; 6 August [O.S. 27 July] 1667 – 1 January 1748) was a Swiss mathematician and was one...

In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success"...

Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. Bernoulli's principle states that an increase in the...

Bernoulli family of Basel. Bernoulli differential equation Bernoulli distribution Bernoulli number Bernoulli polynomials Bernoulli process Bernoulli Society...

probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution...

In probability and statistics, a Bernoulli process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is...

architect Bernoulli differential equation Bernoulli distribution and Bernoulli random variable Bernoulli's inequality Bernoulli's triangle Bernoulli number Bernoulli...

sequence, primary pseudoperfect number, only number for which n equals the denominator of the nth Bernoulli number, Schröder number 1807 = fifth term of Sylvester's...

228 is the smallest even number n such that the numerator of the nth Bernoulli number is divisible by a nontrivial square number that is relatively prime...

standard for bibliographic references 691 = prime number, (negative) numerator of the Bernoulli number B12 = -691/2730. Ramanujan's tau function τ and the...

success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i...

2 {\textstyle B_{1}=+{\frac {1}{2}}} . The Bernoulli numbers have various definitions (see Bernoulli number#Definitions), such as that they are the coefficients...

computer algorithm written by Ada Lovelace that was designed to calculate Bernoulli numbers using the hypothetical analytical engine. Note G is generally...

In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series...

the fifth irregular prime, because it divides the numerator of the Bernoulli number B 24 = − 236364091 2730 = − 103 ⋅ 2294797 2730 . {\displaystyle B_{24}=-{\frac...

needed] Bell number Bernoulli number Dirichlet beta function Euler–Mascheroni constant Jha, Sumit Kumar (2019). "A new explicit formula for Bernoulli numbers...

\left({\frac {z}{2}}\right)=1-B_{2}{\frac {z^{2}}{2!}}+\cdots } where the Bernoulli number B 2 = 1 6 . {\displaystyle B_{2}={\frac {1}{6}}.} (In fact, ⁠z/2⁠ cot(⁠z/2⁠)...

Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) is a simplification of the linear theory of elasticity which...

constant negative Gaussian curvature, by the uniformization theorem. The Bernoulli number B 1 {\displaystyle B_{1}} has the value ± 1 2 {\displaystyle \pm {\tfrac...

Napier. The Swiss mathematician Jacob Bernoulli discovered the constant while studying compound interest. The number e is of great importance in mathematics...

In mathematics, an ordinary differential equation is called a Bernoulli differential equation if it is of the form y ′ + P ( x ) y = Q ( x ) y n , {\displaystyle...

B n ( x ) {\displaystyle B_{n}(x)} is a Bernoulli polynomial. B n {\displaystyle B_{n}} is a Bernoulli number, and here, B 1 = − 1 2 . {\displaystyle...

numerator of any of the Bernoulli numbers Bk for k = 2, 4, 6, ..., p − 3. Kummer's proof that this is equivalent to the class number definition is strengthened...

{1}{n^{k-1}}}-1\right)+R_{m,n},\end{aligned}}} where B k {\displaystyle B_{k}} is a Bernoulli number, and Rm,n is the remainder term in the Euler–Maclaurin formula. Take...

where: B n {\displaystyle B_{n}} is the nth Bernoulli number E n {\displaystyle E_{n}} is the nth Euler number The following expansions are valid in the...