# Questions tagged [difference-equations]

Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.

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### How to directly convert the solution of a recursive equation into a function expression? [closed]

Clear["Global*"] RSolve[{p[i] == 2/5 p[i - 1] + 1/2 p[i] + 1/10 p[i + 1], p[0] == 0, p[8] == 1}, p[i], i] // FullSimplify According to the above ...
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90 views

### Sigma Delta Modulator in Mathematica

Below code is for 1st order sigma delta modulator used in ADC/DAC circuits. ...
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### Finding the general formula for the sequence defined by $u_1 = 1$ and $u_{n+1} = u_n + 1 + \sqrt{u_n+3}$

Let be given sequence $(u_n)$ satisfying: $$u_1 = 1, \quad u_{n+1} = u_n + 1 + \sqrt{u_n+3}, \forall n \geq 1.$$ I tried ...
• 4,317
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### Recursion not working

I am trying to find the terms x7,x8,x9 and so on from the recursive relation given in the code. ...
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### How to solve recurrence equation using RSolve?

How can I solve the following recurrence equation while I dont have the initial values? Is it possible to solve this using RSolve? ...
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### Recurrence formula evaluating with speacial counting of subscripts

Hoping to check some recurrance relationship like this $a_1 = x$ and $a_2 = y$, with $$a_{2n+1} = a_{2n} a_{2n-1}$$ and $$a_{2n+2} = a_{2n+1} + 4$$ Tried ...
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### How to find the general term formula of this sequence? [closed]

Note that S [n] is the sum of the first n terms of the sequence a [n]. It is known that a [1]==1, and the sequence {S [n]/a [n]} is an equal difference sequence with a tolerance of 1/3. Find the ...
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1 vote