Important help on the subject of polynomials of binomial arrangement

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Hi, everyone
It is known that binomial distribution can also be solved by polynomials. i add document with a question I can not solve.

Glad to get for help

Thanks to all the respondents
 

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Welcome issue, in order to get help with this it would be better if it was posted in the Homework section, even if it's not actually homework. General Discussion is not the place for it.

You can repost in the proper homework section here https://www.physicsforums.com/#homework-help.260

Be sure to fill out the template provided an show what you have already done to solve the problem yourself so that people know what you've already tried and where they should start.
 
Hello everyone, I was advised to join this community while seeking guidance on how to navigate the academic world as an independent researcher. My name is Omar, and I'm based in Groningen The Netherlands. My formal physics education ended after high school, but I have dedicated the last several years to developing a theoretical framework from first principles. My work focuses on a topological field theory (which I call Swirl-String Theory) that models particles as knotted vortex...

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