Bernoulli numbers and solitons

Abstract

We present a new formula for the Bernoulli numbers as the following integral $$B_{2m}=\frac{(-1{)}^{m-1}}{2^{2m+1}}{\int }_{-\infty }^{+\infty }(\frac{d^{m-1}}{d{x}^{m-1}}{sech}^{2}x{)}^{2}dx.$$ This formula is motivated by the results of Fairlie and Veselov, who discovered the relation of Bernoulli polynomials with soliton theory.

5 pages

Cited by in corpus (3)

• On some connections between the Gompertz function and special numbers
• On the combinatorics of several integrable hierarchies
• Set partitions and integrable hierarchies