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The microscopic wave functions of the composite fermion theory canincorporate electron mass anisotropy by a trivial rescaling of the coordinates.These wave functions are very likely adiabatically connected to the actual wavefunctions of the anisotropic fractional quantum Hall states. We show in thisarticle that they possess the nice property that their energies can beanalytically related to the previously calculated energies for the isotropicstates through a universal scale factor, thus allowing an estimation of severalobservables in the thermodynamic limit for all fractional quantum Hall states.The rather weak dependence of the scale factor on the anisotropy providesinsight into why fractional quantum Hall effect and composite fermions arequite robust to electron mass anisotropy. We discuss how better, though stillapproximate, wave functions can be obtained by introducing a variationalparameter, following Haldane [Phys. Rev. Lett. {\bf 107}, 116801 (2011)], butthe resulting wave functions are not readily amenable to calculations. Ourconsiderations are also applicable, with minimal modification, to the casewhere the dielectric function of the background material is anisotropic.

Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect