Symmetry of Bernoulli Polynomial

Theorem
Let $B_n \left({x}\right)$ denote the nth Bernoulli polynomial.


 * $B_n \left({1 - x}\right) = \left({-1}\right)^n B_n \left({x}\right)$

Proof
Let $G \left({t, x}\right)$ denote the Generating Function of Bernoulli Polynomials.

Then:

Thus: