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 Λ quite different from that in BCS theory. Using Leggett's theory, as modified for heavy fermions, it is possible to extract from the measured temperature dependence of Λ 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 electronic specific heat C(el), related to that of Λ, is also expected. We have carefully determined the magnitude and temperature dependence of Λ in CeCoIn(5) by muon spin relaxation rate measurements to obtain F(0)(s) = 36 ± 1 and F(1)(s) = 1.2 ± 0.3, and we find a consistent change in the temperature dependence of C(el). This, the first determination of F(1)(s) with a value ≪ 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.