Hi every one, 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)!)
Please enter your typed Mathematica code, not a photographic image, in your post.
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Aha. you can be sure Sir that If someone answered my problem correctly I will mention the correct answer here. And I am sorry I did not know community guideline. thanks a lot
By taking one (or both) of the parameters a and b to be approximate reals, e.g., a=1. rather than a=1, or by taking N of the entire expression, I get with Mathematica (12.1) the value 1.38785.
I suggest you separately define those coefficient functions a[p_, k_]:= ... and b[q_, n_, k_] : = ....
Then evaluate them for sample values of their arguments to see if you’re getting what you expect.
If so, then make your entire expression much simpler to check by using a[p, k] and b[q, n, k] in them rather than the much longer, harder-to-read expressions you have now.
P.S. Why do you believe the correct answer should be 0.119 (approximately)?
Are you sure that the terms in the power series involved decrease in magnitude quickly enough so that 30 terms suffice?
Yes, after 20 terms the expression gives almost the same answers.
This expression is originally an integration expression. So from the integration we get the value 0.119. But the integration is very hard when a > 1. That is why I tried to get a numerical form for soing so.
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.
