I saw a video from GradeAunderA. He said he discovered this formula

Hilariously enough he complains about people using "big words", yet it's okay for him to come up with useless formulas.

I could take his formula and use trivial exponents rules to make it even bigger.

That means I am smarter than him.

>doesn't tip
>complains about big words
>gets in youtube fights

dudes a pleb

I see a lot of shit talking in this thread and yet nobody has a derivation of this formula

he said he just sat and looked at the numbers until he found something that worked

Why bother, I am smarter than him.

My formula is larger and I can make it even larger, just keep applying logs!

>>doesn't tip
He's British

Derivation turns out to be trivial. Starting with the inner most exponentiation
[math]x^{ \frac{m*\log y}{\log x} - n} = e^{\log x * \left( \frac{m*\log y}{\log x} - n\right)} = e^{m*\log y - n\log x} = e^{\log y^m}e^{\log x^{-n}} = y^mx^{-n}[/math]

So then we may rewrite the whole LHS to be
[math]x^{n + \frac{\log \left( 1 + y^m x^{-n} \right)}{ \log x }} = e^{\log x * \left(n + \frac{\log \left( 1 + y^m x^{-n} \right)}{ \log x }\right) } = e^{n*\log x + \log x * \frac{\log \left( 1 + y^m x^{-n} \right)}{ \log x } } = e^{\log x^n + \log (1 + y^mx^{-n})}[/math]

Continuing from the last line
[math]e^{\log x^n + \log (1 + y^mx^{-n})} = e^{\log x^n}e^{\log (1 + y^mx^{-n})} = x^n (1 + y^mx^{-n}) = x^n + y^m[/math]

As desired.

forgot to add from vitriol to my derivation

a literally highschooler (grade 8-9? I forget) could do this as soon as they learn the properties & definitions of the log and exponentiation functions.

>claims he discovered a formula that baffled mathematicians
>impresses audience

this just goes to show that the audience is at most 13-14 years old

He says it holds for all x,y,m,n in R. Was he even trying?

lewl what a fucking meme of a human trashcan. evidentally he put 0 thought into his fraud since [math]\log 0[/math] is undefined

Bet you can't derive this big boy.
That's the thing about math, you can laugh at those below you but when someone above you shows up, you run away crying. Best that nobody laughs at anybody.

he couldn't be fucked to even put his magic meme formula into wolfram

my point wasn't to "show him up" but instead show that someone in highschool could figure this out

he straight up lied if he claims that this "formula was thought not to exist" or if he claims that it "surprised mathematicians"

it's like taking a screencap of your trigonometry homework and claiming you're euclid

You derive it knowing already the conjecture/answer. Coming with it by your own isn't as trivial, but yea, he probably bullshited that part of being the first one.

these exercises are just exercises in patience and highschool algebra, assuming you know the basic identities

this "magic meme formula" is a consequence of the infinite series representation of [math]\phi[/math]

[math]\phi = \frac{13}{8} + \sum^\infty_{n = 0} \frac{(-1)^{(n + 1)}(2n + 1)!}{(n + 2)!n!4^{(2n + 3)}}[/math]

mathematics isn't about who can obfuscate an identity in a non-obvious way

>babby is desperate to be ramanujan

i mean saying it's not trivial is like saying

x = e^(log x) = e^( log x + y - y) = e^(log x + e^log y - x^((log y)/log(x)) ) = ... etc ...

is not trivial. He just messed up the terms with basic highschool identities until he felt it was sufficiently complicated enough to fool kids with his magic meme formula

I'm pretty sure my series is a new discovery. Want to take my up on that claim? You can try deriving it, searching the literature, do whatever you want I've always wanted to know.

What makes it extra special is that I've only ever seen one other infinite series representation for the golden ratio

he might very well have been the first one, but it's not a meaningful result. i might very well have been the first one to write

2 = 1 + 1 + 7 - 7 + 3 - 4 + 5 + 2^2 - 5^3 + 3^4 + 36

but who gives a shit?

he basically did this exact thing but with highschool identities instead of numbers, working identity by identity until he felt done

>working identity by identity until he felt done
Which makes me wonder why did he stop there? What was he even trying to do?

Maybe it is indeed new, and if you truly just "saw" it then I'd say that's impressive (assuming it's right, I don't feel like checking). However, it's impressive in the way that memorizing 100 000 digits of pi is impressive, not in the sense that proving Fermat's last theorem is impressive . I don't know how much use it'll be in "serious" mathematics, but certainly it gives you an edge when investigating new topics with a first/intuitive glance

see
> He just messed up the terms with basic highschool identities until he felt it was sufficiently complicated enough to fool kids with his magic meme formula

Holy shit user, you searched wikipedia, found a series and just assumed my series to be the same? Seriously? If you even spent two seconds comparing them you will see that they have absolutely nothing to do with each other. Go on try deriving my series from that you fucking idiot. Precisely what I am saying that Veeky Forums is quick to laugh at others when they are idiots themselves.

>literally not understanding the definition of 'consequence'

let me help you out
[math]\text{a consequence of} \neq \text{is precisely equal to}[/math]

cretin desperate to save face

Jesus Christ, are you still butthurt about this useless series expansion?

Except even that is wrong, the two series have absolutely nothing to do with each other. Prove your bullshit claims. Show how its a consequence of that other series.

but x is on both sides?

also why not just leave it as x and y lol why make it so complicated

I'm not "butthurt" about it I am pointing out that it's still possible for amateurs to derive things that aren't trivial to re-derive. Saying "lol it's useless" won't make up for the fact that you can't derive it. Since when was number theory useful anyway?

Veeky Forums attacks low hanging fruit, laughing at youtube popscientists, come on that's just sad. Attack someone who actually knows something about number theory, like me. I'm here waiting.

what is your definition of a number? (I'm not a maths student)

It's just [math]2^{x/2} \cos{ \frac{\pi x}{4} } = \sum_{n=0}^\infty \binom{x}{n} \cos{\frac{\pi n}{2}}[/math] with [math]x=\frac{4}{5}[/math].
Surprise, it's a trivial series expansion.

See Wildberger
Wrong.

>Wrong.
not even that guy
but it's literally this you retard, just plug it i and its exactly the same

>taking a screencap of your trigonometry homework and claiming you're euclid
I did that once! Granted I'm a pseudointellectual attention-seeking roast stacy cunt who honestly doesn't understand the difference

Check my instagram it's full of math drawings im such a nerd omg

You're an actual mongoloid its not the same thing.

The result is not interesting, even from a number theory standpoint. The proof might possibly be, but you always refuse to share it because someone might steal it or something. Also, useful is relative to its use in, say, better understanding or solving other problems in number theory. Some one off infinite series reveals no greater structure, and is roughly on par with the OP.

It's exactly the same thing.

Found the kissless virgin

The LHS wasn't the same unless he misformatted the latex. And running something through a computer program to find an alternate expression does not maketh a proof. All you've done was verify it.

>The result is not interesting, even from a number theory standpoint
There are not many infinite series expressions for phi. It's an addition to the literature. My professors were interested but of course an anonymous neckbeard on Veeky Forums knows more than them.
> but you always refuse to share it because someone might steal it or something
Nope I just lost it. I was trying to publish it in some undergrad journal or something but I ended up switching courses, lost contact with professors and i cleared out my harddrive. anyway if it's so trivial why do you need me to provide a proof?
With me and the OP you could have just said "cool" and left it at that but you all went full elitist "attacking it's "intellectual usefulness" and generally acting like insecure dicks. Constantly putting down others is a sign of insecurity.

>running something through a computer program to find an alternate expression does not maketh a proof
the trigonometric identity is well known
all you did was take a special case and pretend like it was revolutionary

I never claimed it was trivial to derive, and I'm merely annoyed by your constant victimized attitude and smugness about the fucking golden ratio.

This thread got sidetracked by some childish troglodyte who desperately wants to be legitimized by some mathematical community despite (likely) doing shit in school.

1- math is not about who can make ugly ass formulas and hiding a basic result in a nested set of identities
2- it's pathetic you're looking for mathematical acceptance from Veeky Forums. Of literally all the possible communities you decided to cry and bite on a Ugandan tire recycling imageboard. Truly tragic. Take a look at your life

But most importantly, this thread was never about whether or not basement dwelling dropouts can produce mathematics or not. It was about how GradeAunderA deliberately and provably lied about his result, as has been shown in this thread. No legitimate mathematician would claim this result "wasn't thought to exist". He couldn't even be fucked to find the correct domain.

GradeAunderA, just like the human trashcan who is seeking legitimacy on Veeky Forums, is a waste of oxygen

>He got a maths degree
And here I was wondering, how can someone be such a spergie

Why are you so mad ?

>being this triggered

I think he's VeganGains; still butthurt about that asspounding Grade gave him.