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A difference equation related to RW on Hypercube
I am trying to solve the following recurrent relation
$$
T(n)=\frac{n}{m}T(n-1)+\frac{m-n}{m}T(n+1)+1, \,\, \text{subject to } T(m)=0
$$
Where $0\leq n\leq m$ and $m$ is a fixed integer. I have ...
