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We present the ${\cal O}(\lambda^3)$ results from the $\lambda$ expansion inthe extremely correlated Fermi liquid theory applied to theinfinite-dimensional $t$-$J$ model (with $J=0$), and compare the results withthe earlier ${\cal O}(\lambda^2)$ results as well as the results from thedynamical mean field theory. We focus attention on the $T$ dependence of theresistivity $\rho(T)$, the Dyson self energy, and the quasiparticle weight $Z$at various densities. The comparison shows that all the methods displayquadratic in T resistivity followed by a quasi-linear in T resistivitycharacterizing a strange metal, and gives an estimate of the different scalesof these variables relative to the exact results.

Extremely Correlated Fermi Liquid theory for $U=\infty$, $d=\infty$ Hubbard model to ${\cal O}(\lambda^3)$