Bernoulli numbers and solitons

Details Bernoulli numbers and solitons Bernoulli numbers and solitons

2005-03-09

arxiv.org/abs/math/0503175v1

Mathematics

General Mathematics

5 pages

Scientific paper

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

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