Bernoulli polynomial


The Bernoulli polynomialsMathworldPlanetmathPlanetmath are the sequenceMathworldPlanetmath {br(x)}r=0 of polynomialsPlanetmathPlanetmath defined on [0,1] by the conditions:

b0(x) = 1,
br(x) = rbr-1(x),r1,
01br(x)𝑑x = 0,r1

These assumptionsPlanetmathPlanetmath imply the identity

r=0br(x)yrr!=yexyey-1

allowing us to calculate the br. We have

b0(x) = 1
b1(x) = x-12
b2(x) = x2-x+16
b3(x) = x3-32x2+12x
b4(x) = x4-2x3+x2-130
Title Bernoulli polynomial
Canonical name BernoulliPolynomial
Date of creation 2013-03-22 11:45:51
Last modified on 2013-03-22 11:45:51
Owner KimJ (5)
Last modified by KimJ (5)
Numerical id 12
Author KimJ (5)
Entry type Definition
Classification msc 11B68
Classification msc 65-01
Related topic BernoulliNumber