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

Thus: