serie zeta

∑ (1/n^{2}) =  (pi^{2}/6)
∑ (1/n^{2}) =  (-1)^{1+1}·pi^{2·1}·2^{2·1+(-1)}·(1/12)
∑ (1/n^{4}) = (pi^{4}/90)
∑ (1/n^{4}) =  (-1)^{2+1}·pi^{2·2}·2^{2·2+(-1)}·(-1)(1/720)
∑ (1/n^{6}) = (pi^{6}/945)
∑ (1/n^{6}) =  (-1)^{3+1}·pi^{2·3}·2^{2·3+(-1)}·(1/30240)
∑ (1/n^{8}) = (pi^{8}/9450)
∑ (1/n^{8}) =  (-1)^{4+1}·pi^{2·4}·2^{2·4+(-1)}·(-1)(1/1209600)
∑ (1/n^{10}) = (pi^{10}/93555)
∑ (1/n^{10}) =  (-1)^{5+1}·pi^{2·5}·2^{2·5+(-1)}·(1/47900160)


∑ (1/n^{2s}) =  (-1)^{s+1}·pi^{2·s}·2^{2·s+(-1)}·B_{2s+(-1)}(0)


on B_{2s+(-1)}(0) és el número de suma de potencies.