Assumption doesn't work in this Sum?

[xkozyra (Maciej Kozyra)]

(Newbie question)

I have mathematical formulas

which I want to implement in Mathematica. I tried with such a command:

A[c_,t_]=Simplify[Sum[v[2*j]^(n)*t^(n+1-2*j),{j,0,c}],Assumptions->n+1-2*j>=0]

and

g[h_,c_]=t+Sum[e^(n/2)*A[c,t],{n,0,h}]

but I obtained

Of course terms with (1/t)^n should not be here based on the assumption. Could you tell me how to solve this problem?

Next question. How can I made a sum without upper bound of summation? As you can see the upper bound of summation in A_n (t) depends also on g(t), which also preclude to write the upper bound explicitly (probably). How to avoid such a problem?

Thank you for your attention and answers.

Best regards,

Maciej Kozyra

[gianlucagorni]

It is not clear to me what your formulas mean exactly. Here is an attempt at interpretation:

a[n_, t_] := 
  Sum[Subscript[\[Alpha], 2]^n t^(n + 1 - 2 j), {j, 0, 
    Min[n, Floor[(n + 1)/2]]}];
g[h_, c_] := t + Sum[\[Epsilon]^(n/2) a[n, t], {n, 0, h}]

[xkozyra (Maciej Kozyra)]

Thank you kindly for your attention! It works perfectly!

However, instead of 2 in the definition of Subscript should be 2*j.

I work on functions only. I understand you have some doubts about that function v[ ] which appeared in my code. This is of course [Alpha] [ ] from mathematical formulas. I apologize for that inaccuracy.

Once again thank you for your help!

Best regards,

Maciej Kozyra