 More precisely, the formula_5 term of the spectral sequence is formula_6, and the spectral sequence converges conditionally to formula_7.Atiyah and Hirzebruch pointed out a generalization of their spectral sequence that also generalizes the Serre spectral sequence, and reduces to it in the case where formula_8.It can be derived from an exact couple that gives the formula_9 page of the Serre spectral sequence, except with the ordinary cohomology groups replaced with formula_10.