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I'm not sure how to calculate the attached equation with these multiple summations implemented into each other......

implemented equation

the variables a, b1, b2 in the last term include all the counters i1, i2 j1, j2: enter image description here

my idea is as follows in the attached img enter image description here

F.Abdullah
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  • variables of a, b1, b2 are: a=N/2- k + i1 +1...........b1=N/2- L + j2 - j1......... b2=L- i2 + j1,,,,,,so all the summation counters are implemented in the last term – F.Abdullah Aug 06 '17 at 05:58
  • Are these all multiplied?? Where on EARTH did you find this thing? – Brevan Ellefsen Aug 06 '17 at 06:16
  • hahaha.....yeah its supposed to be multiplied – F.Abdullah Aug 06 '17 at 06:17
  • Also, please try to show some effort on this question. This is your third post on Math.SE - you should know the drill by now. Show any work you have tried, go to the effort of putting your equation in decent MathJax (doesn't have to be perfect), explain the context of the problem, etc. This is NOT a homework solving site or anything akin to that, though even homework is allowed here if you follow the proper guidelines :) – Brevan Ellefsen Aug 06 '17 at 06:18

1 Answers1

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(Answer modified since the definitions of $a,$ $b_1,$ and $b_2$ have been clarified by providing them in the question itself. I confess I did not recognize them in the question's comments, partly due to the formatting there.)

This is indeed a summation over four variables, which would be computed much the way the question describes (although I think the algorithm could be described a little simpler).

Perhaps you can use properties of the gamma function to simplify the calculation of the last couple of lines of the formula. You can at least rearrange the arguments to the gamma function so that each argument is merely a constant plus one linear term for each of the iteration variables used in that argument.

David K
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  • the variables a, b1, b2 in the last term include ALL the counters i1 ,i2, j1, j2 .....which i have clarified in the first comment – F.Abdullah Aug 06 '17 at 07:54
  • It would have been better to put those definitions in the original question, though now that the question has been edited it is OK. You seem to have understood the calculation procedure correctly. – David K Aug 06 '17 at 13:49