Bernoulli number
RATIONAL NUMBER SEQUENCE 𝐵ₖ SUCH THAT (𝑚+1)∑𝑛ᵐ=(ᵐ⁺¹₀)𝐵₀𝑛ᵐ⁺¹−(ᵐ⁺¹₁)𝐵₁𝑛ᵐ+(ᵐ⁺¹₂)𝐵₂𝑛ᵐ¯¹−(ᵐ⁺¹₃)𝐵₃𝑛ᵐ¯²+⋯
Bernoulli numbers; Bernouilli numbers; Bernouilli number; Bernoulli Numbers; Mohammed Altoumaimi; Akiyama-Tanigawa algorithm; Akiyama–Tanigawa algorithm; Generalized Bernoulli number; Generalised Bernoulli number; Generalized bernoulli number; Generalized Bernoulli numbers; First Bernoulli numbers; Second Bernoulli numbers; Seidel triangle
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain values of the Riemann zeta function.