Y'all I've managed to get past a major fucking huge wall in The Math Problem

The random fucking thing I found on desmos one day literally years ago and I've been obsessed with ever since

I've finally broke through one of the worst hurdles I've been struggling with fucking :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper: :ablobcathyper:

Basically I found an equation for this number: oeis.org/A329458

Which doesn't require the asterisk of ">1" or "!=1"

It just straight up only works for the number itself and nothing else

Even if you evaluate using limits, it's the only one that works!! (This was a problem since a lot of times it'd be undefined at 1, but the limit at 1 was defined... And the CAS I was using didn't seem to care about that difference)

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here's the equation by the way lmao

it's a fucking mess because i had to do weird shit with derivatives and calculus in order to isolate the number away from 1, so i had to make a new function which basically makes the number share the special properties with 0 instead of 1

and then make another new equation in which i use both the original and the modified one together in a system of equations such that only my number solves it

and i had to make the big pain in the ass section just to get a function without 1 being an asshole in it lmao

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if anyone has any suggestion on how to simplify this monstrosity please let me know because dear god it's horrific

but im assuming no one will because a mere glance at that equation is enough to rightfully nope the fuck out

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i have years of hyperfixation on this fucking problem that means that i see this and feel bliss instead because i finally have a fucking equation that uniquely identifies my number

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i was literally shaking earlier when i finally got it to work out lmao

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debating if i wanna update the OEIS page with this identity

because while it is a new one, and the first found that's totally unique to the number

it's an absolute fucking salady mess of nonsense

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like once i knew what i wanted i just started chucking shit in there til it worked out lmao

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