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Define NIntegrate... as a numerical function: nint[uu_?NumericQ] := NIntegrate[(uu/Sqrt[((1/ 3) + (2/9) (Cos[kx] + Cos[(kx + Sqrt[3] ky)/2] + Cos[(kx - Sqrt[3] ky)/2]))^2 + uu^2]), {kx, 0, 4}, {ky, 0,4}] RecurrenceTable[{d[n] == nint[d[n - 1]], d[0] == 1}, d, {n, 1, 10}] (* {15.1676, 15.9952, 15.9957, 15.9957, 15.9957, ...


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