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Trying to write a script to calculate a sum

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Can somebody show me how to write a script to calculate the following function of N? It just confuses me a bit because if N is an even number then it may very well be the the lower and upper index are not integers... I don't know what the best way to deal with this hurdle is, perhaps make the function go from a negative integer to a positive integer then make a necessary substitution??
I'm not sure.. But i'd love to see what you guys come up with. I'm slowly learning how to write basic programs, but this one is a bit out of my league, and I'd appreciate if somebody could show me how
p.s. how do I make the LaTeX formatting turn on??
Michael Vaughan
Michael Vaughan on 26 Sep 2020
The equation is from a reputable source, a paper of
It is implied that you take the sum as j increases by 1 at each iteration of the summation. Since the top and bottom index are opposites of eachother, this is well defined

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Accepted Answer

Alan Stevens
Alan Stevens on 26 Sep 2020
Simply let k = 2j and then you can write:
This will hold for both N even and N odd.

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