n | 0 | 1 1 | x - 1/2 2 | x^2 - x + 1/6 3 | x^3 - (3 x^2)/2 + x/2

n | 0 | 1 | 2 | 3 |

integral B_n(x) dx = (B_(n + 1)(x))/(n + 1) + constant

B_n(x) = ζ(1 - n, x) (-1) n for (n element Z and n>0)

B_n(x) = ζ(1 - n) (-1) n + n H_(x - 1)^(1 - n) for (n element Z and n>0)

B_n(x) = ζ(1 - n, x) (-1) n for (n element Z and n>0 and π + 2 arg(x)>0 and 2 arg(x)<=π)

B_n(x) = sum_(k=0)^n x^k B_(-k + n) binomial(n, k)

B_n(x) = x^n sum_(k=0)^n x^(-k) B_k binomial(n, k)

B_n(x) = -2^(1 - n) π^(-n) n! sum_(k=1)^∞ k^(-n) cos(1/2 π (n - 4 k x)) for (00)

B_n(x) = (-1 + n) n (i/(2 π))^n integral_0^1 (log^(-2 + n)(t) log(1 + t^2 - 2 t cos(2 π x)))/t dt for (0<=x<=1 and n/2 element Z and n>0)

B_n(x) = -2^(1 - n) n π^(-n) integral_0^1 ((-t cos((n π)/2) + cos((n π)/2 - 2 π x)) log^(-1 + n)(1/t))/(1 + t^2 - 2 t cos(2 π x)) dt for (00)

B_n(x) = (-1)^floor(1/2 (-1 + n)) n integral_0^∞ (t^(-1 + n) ((-1)^floor(n/2) cos((n π)/2 + 2 π x) - e^(-2 π t) (1 - n + 2 floor(n/2))))/(-cos(2 π x) + cosh(2 π t)) dt for (00)