Partial Recurrence Equation - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T09:51:39Z http://mathoverflow.net/feeds/question/83645 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83645/partial-recurrence-equation Partial Recurrence Equation riehen 2011-12-16T17:58:03Z 2011-12-16T17:58:03Z <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>