The formation of heavy fermion bands can occur by means of the conversion of a periodic array of local moments into itinerant electrons via the Kondo effect and the huge consequent Fermi-liquid renormalizations. Leggett predicted for liquid $^3$He that Fermi-liquid renormalizations change in the superconducting state, leading to a temperature dependence of the London penetration depth~$Lambda$ quite different from that in the BCS theory. Using Leggetts theory, as modified for heavy fermions, it is possible to extract from the measured temperature dependence of $Lambda$ in high quality samples both Landau parameters $F_0^s$ and $F_1^s$; this has never been accomplished before. A modification of the temperature dependence of the specific heat $C_mathrm{el}$, related to that of $Lambda$, is also expected. We have carefully determined the magnitude and temperature dependence of $Lambda$ in CeCoIn$_5$ by muon spin relaxation rate measurements to obtain $F_0^s = 36 pm 1$ and $F_1^s = 1.2 pm 0.3$, and find a consistent change in the temperature dependence of electronic specific heat $C_mathrm{el}$. This, the first determination of $F_1^s$ with a value~$ll F_0^s$ in a heavy fermion compound, tests the basic assumption of the theory of heavy fermions, that the frequency dependence of the self-energy is much more important than its momentum dependence.
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