Definition:Bernoulli Polynomial

Definition

The Bernoulli polynomials $\map {B_n} x$ are the terms of the sequence of polynomials defined as:

$\ds \map {B_n} x = \sum_{k \mathop = 0}^n \binom n k B_{n - k} x^k$

where $B_k$ are the Bernoulli numbers.

Also see

• Generating Function for Bernoulli Polynomials

• Results about the Bernoulli polynomials can be found here.

Source of Name

This entry was named for Jacob Bernoulli.

Sources

• 1976: Tom M. Apostol: Introduction to Analytic Number Theory: $\S 12.12$ Properties of Bernoulli numbers and Bernoulli polynomials