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 Sep24 awarded Autobiographer Jan3 comment How do I use RSolve to solve a system of recurrence relations? @belisarius I got downvoted for posting the picture! Jan3 revised How do I use RSolve to solve a system of recurrence relations? added 497 characters in body Jan3 comment How do I use RSolve to solve a system of recurrence relations? @belisarius See update. Jan3 comment How do I use RSolve to solve a system of recurrence relations? @belisarius I mean a[n-1] behaves like $\sqrt{\frac{\pi}{2} n}$. Jan3 comment How do I use RSolve to solve a system of recurrence relations? @belisarius In fact it should look like $\sqrt{\frac{\pi}{2} n}$ in the limit. Jan3 comment How do I use RSolve to solve a system of recurrence relations? @belisarius Are you sure the plot of a[n-1] is correct? Here is what I do in Maple and I get a different graph.rsolve({a(1) = 1+2/n, a(p) = 1+(p-1)*a(p-1)/n+2*b(p-1)/n, b(0) = 1, b(p) = 1+pb(p-1)/n}, {a(p), b(p)}); subs(p = n-1, %); I then copy the answer for a(n-1) and do plot([seq([n, (1/n)^(n-1)*nGAMMA(n-1)*(Sum((n+2*(1/n)^p1*exp(n)*GAMMA(p1+1, n))/(n^2*(1/n)^(p1+1)*GAMMA(p1+1)), p1 = 1 .. n-2)+1+2/n)], n = 2 .. 200)], style = point) Jan1 comment How do I use RSolve to solve a system of recurrence relations? Thanks very much. Jan1 comment How do I use RSolve to solve a system of recurrence relations? Thanks but isn't it possible to use the answer to RSolve[{ a[p] == Evaluate[b[p] /. h[[1]]] + ((p - 1)/n) a[p - 1], a[1] == 1 + 2/n}, {a[p]}, p] without having to retype the answer for a[n]? Jan1 comment How do I use RSolve to solve a system of recurrence relations? Thanks. How can I now do the substitution and plotting? If there isn't a bug then it should look like $\sqrt{n}$. Jan1 comment How do I use RSolve to solve a system of recurrence relations? Sorry... copy and paste error. I have the same problem with RSolve with a capital S. Is there a way to restart so that there are no existing function/variable settings or is there some other reason it doesn't appear to do anything? Jan1 revised How do I use RSolve to solve a system of recurrence relations? edited body Jan1 asked How do I use RSolve to solve a system of recurrence relations? Dec28 revised Solve pair of recurrence relations added 353 characters in body Dec28 revised Solve pair of recurrence relations added 8 characters in body Dec28 comment Solve pair of recurrence relations user141063 Thanks! Shouldn't Rsolve be able to solve it explicitly? Dec28 revised Solve pair of recurrence relations added 247 characters in body Dec28 revised Solve pair of recurrence relations added 7 characters in body Dec28 comment Solve pair of recurrence relations Yes that is what I am looking for. Dec27 awarded Commentator