# RSolve with simple initial condition

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 $m-1$?

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