Since my freshman year of high school, when I became increasingly bored with school math, I would look up things on my own which interested me. More than that, I would play around with them. Continued fractions? Sounds interesting - now let’s try and see if I can derive a closed form if I vary the parameters this way. Sums involving the harmonic number? Let’s see if I can generalize them with another parameter. Of course, I didn’t find anything truly interesting for a very long time - I would find out that what I’d done had been done two hundred years ago, in a much simpler way. But eventually, I hit gold - and it turned into this very project. I knew absolutely nothing about number theory when I started - I was working with polynomial roots at first, and only later did I realize I was staring at functions I’d seen in number theory.

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• Mathematics