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Problem in finding out the root of the equation with sums

Posted 8 years ago
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I am facing the problem in finding out the root of the equation. Feedback is appreciated.

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POSTED BY: Maha haroon
2 Replies
Posted 8 years ago

Perhaps use Simplify to handle the denominators.

In[1]:= Clear[m, k, l, a, b, A, B];
simp = Simplify[1/Sum[Binomial[m-k, l]*(-1)^l*Gamma[k+a]/(        b + B + k/A^2)^(k+a), {l, 0, m-k}]*
                  Sum[Binomial[m-k, l]*(-1)^l*Gamma[k+a]/(1/L^2 + b + B + k/A^2)^(k+a), {l, 0, m-k}]];
m = 35; k = 32; \[Lambda] = 1; a = 2; b = 2; u = RandomReal[UniformDistribution[{0, 1}], m];
t = ((-1*\[Lambda])/Log[u])^(1/2); s = t; w = Sort[s]; st = Take[w, k]; B = Total[st^-2]; A = Last[st];
FindRoot[simp == 0.25, {L, 1}]
FindRoot[simp == 0.75, {L, 1}]
Plot[{simp - 0.25, simp - 0.75}, {L, 0, 3}]

Out[4]= {L -> 0.72545}

Out[5]= {L -> 1.60547}

enter image description here

Please check this carefully. Thank you

POSTED BY: Bill Simpson

The cover posting for a notebook should include a summary of the problem and a clear question.

In this case, both of the Sums add to zero so your equation is 0/0 == 0.25. It may be that the limits on the sums are not correct.

Please try evaluating pieces of the equation separately to find where it goes astray.

Moderation Team

POSTED BY: Moderation Team
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