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enter image description here

I failed to do the following expression and make it give accurate results if any one can help me I will be glade. I attached my expression in a pic "want this" and my trial as "my trial". the correct answer must equal 0.119 when a=1, b=10, m=3, n=6. thanks a lot in advance.

a = 1
b = 10
m = 3
n = 6
a^1 b^n (Sum[
Sum[Sum[Sum[(-1)^(k + v - n + m + 1)
     If[k == 0, 1, 
     SeriesCoefficient[Series[(-Log[1 - x])^k, {x, 0, 30}], 
      p + k]] If[n - k - 2 == 0, 1, 
     SeriesCoefficient[
      Series[(-Log[1 - x])^(n - k - 2), {x, 0, 30}], 
      q + (n - k - 2)]]
    Binomial[n - m - 1, k] Binomial[b - 1, 
     v] (-PolyGamma[0, -1 + 1/a - k + n + q] + 
       PolyGamma[0, 2/a + n + p + q + v])/(a (1 + k + p + v) + 
       1), {q, 0, 30 - (n - k - 2)}], {p, 0, 30 - k}], {v, 0, 
  b - 1}], {k, 0, n - m - 1}])/((m - 1)! (n - m - 1)!)
ramy aldallal
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    You haven't provided a specific question in your question. Also, this is a mess of single-letter variables, I'd consider it unreadable. To debug it and find the problem you have, I'd suggest that your first step be to clean it up, use more descriptive variable names, and break things out so that you don't have just one big expression. – Thomas Jager May 26 '20 at 17:51
  • The problem is not as much the single-letter variables, which are OK in a math context. But you/us would read your code with more ease if you try to format it (use whatever indentation rules are common in the language). And including the image would also help. I don't know the language but there is at least one typo, and two points I would check further. Typo: you have "a^1" while on the notes you have "a^2". I would double check if the summation limits for p (30 - k) and q (30 - (n - k - 2)) are equivalent to infinity. Can you explicitly say "infinity". Or maybe try a fixed "huge" limit? – Rolazaro Azeveires May 26 '20 at 18:25
  • @Bill, the matching ] is at "{q, 0, 30 - (n - k - 2)}]" (the sum limits), I think (with emacs' help) – Rolazaro Azeveires May 26 '20 at 18:26
  • please every one press on " enter image description here" to see the original problem> and for infinity you can see that after 30 for the expression the results are almost the same. – ramy aldallal May 26 '20 at 18:37
  • please every one press on " enter image description here" to see the original problem. and for infinity you can see that after 30 for the expression the results are almost the same. Also, there is an a in the denominator that goes with one of the 2 a's from the numerator. thank you all for your observations and I need more please. – ramy aldallal May 26 '20 at 18:44

1 Answers1

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I found the solution for the problem. the problem was when the value of k was 0 the coefficient will not equal 1 but the whole expression must be found from the start for a value of k that will start from 1 and an expression when the value of k is 0. yet I failed to solve it using MATHEMATICA but by doing the above I succeed to get the correct result. thank you all for your precious time and opinions.

ramy aldallal
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