We present series representations for some mathematical constants, like gamma, pi, log 2, zeta(3). In particular, we prove that the following representation for Euler's constant is valid: [GRAPHICS] established the smallest number M which make the following equality (K) over bar (sigma)(U(W-2(alpha)), M(W-2(alpha)), L-2(R-d)) = (d) over bar (sigma)(U(W-2(alpha)), L-2(R-d)) hold, where U(W-2(alpha)) is the Riesz potential or Bessel potential of the unit ball in L-2(R-k) and the notations (K) over bar (sigma)(.,., L-2(R-d)) and (d) over bar (sigma)(., L-2 (R-d)) denote respectively the relative average width in the sense of Kolmogorov and the average width in the sense of Kolmogorov in their given order. In 2001, Subbotin and Telyakovskii got similar results on the relative width of Kolmogorov type. We also proved that (K) over bar (sigma)(U(W-2(alpha)) boolean AND B(L-2(R-d)), U(W-2(beta)) boolean AND B(L-2(R-d))L-2(R-d)) = (d) over bar (sigma)(U(W-2(alpha)), L-2(R-d)), where 0 < beta < alpha.
