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I am having some trouble with this function

Subscript[f, \[Pi]] = {0.0924, 0.00025};
Pade[x_, n_, m_] :=Sum[Subscript[a, i]*(x)^i, {i, 0, n}]/(
1 + Sum[Subscript[a, i]*(x)^(i - n), {i, n + 1, n + m}]) /. 
Subscript[a, n + m] -> Subscript[a, n]/(2 Subscript[f, \[Pi]][[1]])

Then, this function works ok but all x values but 0, which gives back

In[226]:= Pade[0, 0, 1]
During evaluation of In[226]:= Power::indet: Indeterminate expression 0^0  encountered. >>
Out[226]= Indeterminate

However it works ok if I do

In[228]:= Pade[x, 0, 1] /. x -> 0
Out[228]= Subscript[a, 0]

Any idea why is this? Indeed the kind of indetermination, 0^0 it's freaking me out, theres no such a power law in my function definition, so I don't have a clue of why is this happening ...

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Don't you have x=0, i=0 in the numerator ? –  b.gatessucks Nov 1 '12 at 11:10
    
No, the denominator goes as 1 + a_1x + a_2x^2 + ... –  pablo Nov 1 '12 at 11:13
    
Hey…Subscript[a, i]*(x)^i apparently contains 0^0 when x=0, i=0. –  xzczd Nov 1 '12 at 11:15
    
In the numerator the sum on i starts at 0. –  b.gatessucks Nov 1 '12 at 11:15
    
I just found out what's the problem, the problem is that in the numerator I have Subscript[a,0]x^0 This leads to 0^0 ... When you tell Mathematica to take the limit Limit[Pade[x,0,1],x->0] it performs ok ... now I jast took the Subscript[a,0] parameter outsude the sum and works fine, however I wonder whether I could do it other way ... –  pablo Nov 1 '12 at 11:16
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1 Answer

Since the problem was the evaluation at x=0 - which for the term x^0 gave 0^0 - by taking the term out of the summation the wanted result was obtained:

Subscript[f, \[Pi]] = {0.0924, 0.00025}; 
Pade[x_, n_, m_] := 
 Subscript[a, 0] + 
   Sum[Subscript[a, i]*(x)^i, {i, 1, n}]/(1 + 
      Sum[Subscript[a, i]*(x)^(i - n), {i, n + 1, n + m}]) /. 
  Subscript[a, n + m] -> Subscript[a, n]/(2 Subscript[f, \[Pi]][[1]])

now

Pade[0, 0, 1]

(*Subscript[a, 0]*)
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