I use the code
fv = RecurrenceTable[{a[i] ==
1/(i (i + 1)) (1/Sqrt[w] a[i - 1] + (2 i - 1 - e[i]) a[i - 2]),
a[2] == 1/6 (1/(2*w)+3 - e[i]), a[1] == 1/(2 Sqrt[w])}, a, {i, 3, 10}];
to evaluate the three-step recursion relation where
e[i_]:=e[i]=2i+1
after that I need to obtain the roots of fv, so I use
sol2 = N[Solve[fv[[1]] == 0, w]]
my main problem is that e must be calculated using max i, namely the code must calculate the value of e first, then must use i to calculate recursion relation, For example for i=3 , e becomes 7, then a[3] must be calculated that includes e[3] and a[2] and a1, where a[2] must be calculated using e[3] again not e[2], maybe some sort of a loop needed. I really don't know how to address this problem. Any idea?
The correct results for what I intend are:
i=3, w=0.05;
i=4, w=0.0182 and w=0.1900;
and so on.
You can see the original paper which has introduced the above formula and the results here. I have marked important formula. The results have been shown in the table.
a[i]
is computed usinge[i]
everywhere, even fora[i-1]
etc.? $\endgroup$w
in the question fori = 4
? Please show the equation you solved. $\endgroup$