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We present the results for the low energy properties of the infinitedimensional t-J model with $J=0$, using $O(\lambda^2)$ equations of theextremely correlated Fermi liquid formalism. The parameter $\lambda \in [0,1]$is analogous to the inverse spin parameter $1/(2S)$ in quantum magnets. Thepresent analytical scheme allows us to approach the physically most interestingregime near the Mott insulating state $n\lesssim 1$. It overcomes thelimitation to low densities $n \lesssim .7$ of earlier calculations, byemploying a variant of the skeleton graph expansion, and a high frequencycutoff that is essential for maintaining the known high-T entropy. Theresulting quasiparticle weight $Z$, the low $\omega,T $ self energy and theresistivity are reported. These are quite close at all densities to the exactnumerical results of the $U=\infty$ Hubbard model, obtained using the dynamicalmean field theory. The present calculation offers the advantage of generalizingto finite $T$ rather easily, and allows the visualization of the loss ofcoherence of Fermi liquid quasiparticles by raising $T$. The present scheme isgeneralizable to finite dimensions and a non vanishing $J$.

Low energy physics of the t-J model in $d=\infty$ using Extremely Correlated Fermi Liquid theory: Cutoff Second Order Equations