Xerl[b_, a_] :=
Module[{b2, s, n, x},
  b2 = 1;
  s = 1/a;
  For[x = s, b2 > b, x+=s,
      b2 /= x + b2];
  x -= s;
  n = x*a - 1;
  x /. FindRoot[Berld[x, a] == b, {x, {n, n+1}}]
] /; (0 < b < 1)