We apply the recently developed extremely correlated Fermi liquid theory to the Anderson impurity model, in the extreme correlation limit. We develop an expansion in a parameter lambda, related to n_d, the average occupation of the localized orbital, and find analytic expressions for the Greens functions to O(lambda^2). These yield the impurity spectral function and also the self-energy Sigma(omega) in terms of the two self energies of the ECFL formalism. The imaginary parts of the latter, have roughly symmetric low energy behaviour (~ omega^2), as predicted by Fermi Liquid theory. However, the inferred impurity self energy Sigma(omega) develops asymmetric corrections near n_d ~ 1, leading in turn to a strongly asymmetric impurity spectral function with a skew towards the occupied states. Within this approximation the Friedel sum rule is satisfied but we overestimate the quasiparticle weight z relative to the known exact results, resulting in an over broadening of the Kondo peak. Upon scaling the frequency by the quasiparticle weight z, the spectrum is found to be in reasonable agreement with numerical renormalization group results over a wide range of densities.
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