Question: Iterated Equation Solving Process

Hallo thar. I’m new to both Maple and programming. I’ve been searching for a Maple programming introduction online that would allow me to work on the following problem but haven’t turned up anything.  Hoping some of you can point me in the right direction.


I have two sets of integers {Y1,Y2..Yn} and {B1,B2…Bn}. For each value in the Y set I need to solve a function F(x) for a number of iterations given by the B value corresponding to the Y value (B1 for Y1).

The initial function is F(x) = x*ln((Y+1)/Y)-1.

The solution X1 is the first positive integer to yield F(x) ≥ 1. 

Each iteration subtracts the value of F(x) evaluated at the preceding iteration’s X solution from the initial function.

Then repeat this iteration process for all the values in Y1…Yn. The solution set of Xs for each Y value is then merged into a single set {X values for Y1,X values for Y2…X values for Yn}.


Example of Iterations

Iteration 1 for Y1

F(x) = x*ln((Y1+1)/Y1)-1

Giving solution X1.

Iteration 2 for Y1

F(x) = x*ln((Y1+1)/Y1) - 1 - F(X1)

Which simplifies to F(x) = ln((Y1+1)/Y1) * [x-X1]

Giving solution X2.

Iteration B for Y1

F(x) = ln((Y1+1)/Y1) * [x-X(B-1)]

Giving solution XB.


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