added formulas for zeta values

data/Special_values/Values_of_the_Riemann_zeta_function_at_rational_numbers/collection.yaml

@@ -22,6 +22,14 @@ Comments:
     At $s=0$, $\zeta$ has a simple pole.
   
 Formulas:
+  formula-values-at-non-positive-integers: >
+    $\zeta(-n) = (-1)^n\frac{B_n}{n+1}$ for integers $n\geq 0$, 
+    where $B_n$ is the $n$'th Bernoulli number 
+    with sign convention $B_1=-1/2$.
+    
+  formula-values-at-positive-even-integers: >
+    $\zeta(2n) = \frac{(-1)^{n+1}B_{2n}(2\pi)^{2n}}{2(2n)!}$ 
+    for positive integers $n$.
 
 Programs: 
   program-sage: