New answers tagged difference-equations
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Sigma Delta Modulator in Mathematica
Use memoization of evaluated function values to avoid repeated identical recursion:
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Finding the general formula for the sequence defined by $u_1 = 1$ and $u_{n+1} = u_n + 1 + \sqrt{u_n+3}$
It could be that there is a closed form solution. Following considerations demonstrate that it cannot be simple. Important message is that $u_n$, besides quadratic grows demonstrated in the other ...
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Finding the general formula for the sequence defined by $u_1 = 1$ and $u_{n+1} = u_n + 1 + \sqrt{u_n+3}$
We can find an asymptotic solution by
AsymptoticRSolveValue[{u[n + 1] == u[n] + 1 + Sqrt[u[n] + 3], u[1] == 1}, u[n], {n ,Infinity,3}]
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1
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Accepted
Recursion not working
You can get them by repeated solving and adding to your list of found x,y:
First define:
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