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Suppose we have the following equation: $$ g_ma_m=r_ma_{m-1} $$ with initial condition $a_L=d$ and $L$ might be negative.

The following command

RSolve[{g[m] a[m] == r[m] a[m - 1], a[-10] == d}, a, m]

gives me

{{a -> Function[{m}, 
  d*Product[r[1 + K[1]]/g[1 + K[1]], {K[1], 0, -1 + m}]]
}}

where K[1] runs from 0 to $m-1$. But shouldn't K[1] runs from -10 to $m-1$?

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  • $\begingroup$ or rather from -10 to m-1 (since the arguments of r[] and g[] are 1+K[1] )? Yes, it should. I think ... $\endgroup$ – Wouter Sep 7 '14 at 14:12
  • $\begingroup$ @Wouter,yes you are right. $\endgroup$ – wdg Sep 7 '14 at 15:48

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