Partial Recurrence Equation - MathOverflow most recent 30 from http://mathoverflow.net2013-06-19T09:51:39Zhttp://mathoverflow.net/feeds/question/83645http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/83645/partial-recurrence-equationPartial Recurrence Equationriehen2011-12-16T17:58:03Z2011-12-16T17:58:03Z
<p>Hey people</p>
<p>I have the following equation, which I don't manage to solve.
The background of the problem is the clustergrowth of two chemical species, resulting in a final relation I'd like to solve: </p>
<p>$u_{n,m} = K_\alpha u_{n-1,m} A + K_\beta K_\gamma A B u_{n-1,m-1}$</p>
<p>with the conditions that </p>
<p>$u_{0,0} = S $ </p>
<p>$u_{0,1} = 0$</p>
<p>$u_{1,0} = H_A \cdot A\cdot S$</p>
<p>$K_\alpha, K_\beta, K_\gamma, S$ are constants. $A$ increases $n$ by $1$, $B$ increases $m$ by $1$. </p>
<p>I appreciate your help.
Cheers,
riehen</p>