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We present a framework for the analytic calculations of the hierarchical wavefunctions and the composite fermion wave functions in the fractional quantumHall effect on the sphere by using projective coordinates. Then we calculatethe overlaps between these two wave functions at various fillings and smallnumbers of electrons. We find that the overlaps are all most equal to one. Thisgives a further evidence that two theories of the fractional quantum Halleffect, the hierarchical theory and the composite fermion theory, arephysically equivalent.Comment: 37 pages, revte

Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere