Category: Combinatorics

Bernoulli numbers, Faulhaber’s formula, Umbral Calculus, Volkenborn integrals

Consider the following defining formula for Bernoulli numbers in terms of sums of powers of integers: If we formally think of as this formula becomes The formal replacement of with has many nice properties. For instance, the generating series of Bernoulli numbers can be thought of as The Bernoulli polynomial can seen as Consider the […]