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Elimination of variables with Groebner basis

Posted 1 month ago
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I am trying to solve equations 1 and 3 shown below:

For nmax = 2, I was able to solve for the value of z but higher than that Mathematica keeps on running forever and also I believe at some nmax sum must converge so I am trying to get that value of z.enter image description here,

Could someone simplify the code or suggest some other way to solve for the value of z?

I have attached Mathematica file.

Posted 1 month ago

This problem has been solved.

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