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Sep
24
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Jan
3
comment How do I use RSolve to solve a system of recurrence relations?
@belisarius I got downvoted for posting the picture!
Jan
3
revised How do I use RSolve to solve a system of recurrence relations?
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Jan
3
comment How do I use RSolve to solve a system of recurrence relations?
@belisarius See update.
Jan
3
comment How do I use RSolve to solve a system of recurrence relations?
@belisarius I mean a[n-1] behaves like $\sqrt{\frac{\pi}{2} n}$.
Jan
3
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.
Jan
3
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)
Jan
1
comment How do I use RSolve to solve a system of recurrence relations?
Thanks very much.
Jan
1
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]?
Jan
1
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 $\sqrt{n}$.
Jan
1
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?
Jan
1
revised How do I use RSolve to solve a system of recurrence relations?
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Jan
1
asked How do I use RSolve to solve a system of recurrence relations?
Dec
28
revised Solve pair of recurrence relations
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Dec
28
revised Solve pair of recurrence relations
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Dec
28
comment Solve pair of recurrence relations
user141063 Thanks! Shouldn't Rsolve be able to solve it explicitly?
Dec
28
revised Solve pair of recurrence relations
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Dec
28
revised Solve pair of recurrence relations
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Dec
28
comment Solve pair of recurrence relations
Yes that is what I am looking for.
Dec
27
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