Recurrence Relationsmedium
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Two solutions to a homogeneous second-order recurrence are ϕn(1)=2n\phi_n^{(1)} = 2^n and ϕn(2)=35n\phi_n^{(2)} = 3 \cdot 5^n. Calculate their Casoratian (discrete Wronskian) Wn=ϕn(1)ϕn+1(2)ϕn(2)ϕn+1(1)W_n = \phi_n^{(1)} \phi_{n+1}^{(2)} - \phi_n^{(2)} \phi_{n+1}^{(1)} and determine linear independence.