A Primer on Bernoulli Numbers and Polynomials

Bernoulli numbers and polynomials are named after the Swiss mathematician Jakob Bernoulli (1654–1705), who introduced them in his book Ars Conjectandi, published posthumously (Basel, 1713). They first appeared in a list of formulas (reproduced in FIGURE 1) for summing the pth powers of n consecutive integers, for p = 1 to p = 10. Bernoulli uses the symbol ∫ , an elongated S, to indicate summation. In modern notation his first three examples are equivalent to the familiar relations