Is this worth publishing? It's the only series for the golden ratio that I've ever seen apart from the Fibbonaci definition and the super obvious Taylor expansion of the square root of five.
>>7640434
I've seen you post this 3 times now. At this point if you don't publish it I will.
>>7640434
ask your math prof
>>7640437
You can't publish it without a proof. Also you spend way too much time on such a shitty board.
>>7640443
I have no math prof, dropout
>>7640437
You know what do publish it, I'm not in the maths loop anymore nor do I want to be. I won't give you the proof because if you can come up with it yourself then you deserve credit irregardless of being second. All I will say is trigonometry, binomial theorem and complex analysis. Good luck and goodbye.
brb publishing this
lol a real maths thread and all the self-claimed /sci/ maths geniuses are nowhere to be seen.
>>7640473
inb4 back to leddit
Ask /r/math, there are some actual smart blokes over there.
>>7640591
Good idea, I will.
Unless the method(s) used to compute this are truly new and never been seen before and are useful to solving other problems, this won't get published outside of some high school math club newsletter.
Hate to break it to you. It's good that you're figuring things out on your own, but the math publishing world is quite complicated.
>>7640622
Funny you say that the one time I did mention publishing to a professor he said it was publishable but university maths department newsletter-tier because it was original but not ground-breaking. However to say it's "high school" tier I think you are just trying to look clever by denigrating my work. If you can easily prove it then call it high school tier, otherwise try not to be so condescending. Last time I checked complex analysis and gamma functions aren't taught in high school.
>>7640622
You could publish something like this in an undergraduate math journal easily. Start off with some exposition on the tools used, show how to use them to obtain the result, and there you go.
If it is even true. That the purported identity is being spammed on /sci/ makes me think that this has about the same chance of getting published as that meme proof of abc has of being correct.
>>7640666
lol all you have to do is put both sides in wolfram to see if their numerical values match up
>>7640434
A question for you, OP:
Should the numerator of the second term of the RHS instead read " 4 x 6 " instead of simply "4", or is it correct as-is? Furthermore, by phi do you denote 1.618... = (1+sqrt5) /2, or do you perhaps indicate its negative, reciprocal, or negative reciprocal?
>>7640676
It's just 4
1.618...
>>7640666
How do I do this now that I'm not an undergrad anymore? Can I just choose a university at random and ask to be published in their newsletter?
>>7640666
I said earlier that I didn't want to go back into the maths loop but if it's good for my CV or something maybe it's worth it.
>>7640679
Okay. Then by your "Fibonacci definition" I also infer that you mean that this same phi (1.618...) is equal to the limit as n goes to infinity, of the expression F_n+1 / F_n , and not a series.
Next, if the Taylor expansion of root five is as super obvious as you say, then it can't hurt to, er, expand on that a bit. By the same token it also can't hurt not to.
Third, another alternating series with a leading term exists, which is cited just the same at both wiki and mathworld. The natural thing to do is to compare your series with this one, which I'm thinking about.
Fourth, your series can and should be expressed algebraically, although it involves a nested product, where the above series does not (but for the definition of factorial). Let me think...
>>7640695
I've seen it turned into a series
Just evaluate the Taylor series of f(x) = x^(1/2) at x=5
Interesting, what is it?
Yeah it can it's the ratio of two gamma functions but I totally forgot that part.
>>7640434
I don't think so dude, I'm not into number theory but unless your proof involves something good this would just be another expression in some reference book of identities.
Why did you drop out? You seem creative and good at the subject.
>>7640710
simply visit either site's "golden ratio" page.
The series given at both places is
[math] \displaystyle \phi = \frac{13}{8} + \sum_{n=0}^{ \infty } \frac{(-1)^{(n+1)} (2n+1)! }{(n+2)! \; n! \; 4^{(2n+3)} } [/math]
where phi denotes the same positive quantity greater than one as discussed.
>>7640723
I wasn't doing maths. Why don't I do maths? I don't feel confident enough, I don't feel I will get financial security from it, and I'm generally all round too much of an autistic loser to survive outside of the house. Basically dropped out of the unrelated degree because I was depressed at not fitting in. I browse /r9k/ now. Says it all really.
>>7640721
Yeah man that would be great, that's what I want, I want people to know, I want it added to the list of interesting identities.The proof is bland as fuck, nothing special.
>>7640749
yeah that's the one derived from the taylor series. my professor at the time compared both, he said mine was totally different
>>7640755
oh great, that clears up another question I hadn't yet asked. Meanwhile, I'm still sketching a rewrite of your OP thing...
>>7640752
No one thinks the identities are interesting just so you know. People have those books just in case they need them to solve more interesting problems.
But sure just find a relevant one and send it to the authors I guess.
>>7640767
what, algebraically?
>>7640752
dude, go back to school. even if not a maths major, at least major in physics. you're brilliant.
btw, the above reminds me of number theory. Some interesting expressions are given at Jonathan Sondow's homepage, which appears to be basically unchanged from the last time I looked at it like 12 years ago when it was blowing my mind:
http://home.earthlink.net/~jsondow/
>>7640770
I think it could hold the secret to the series for e^pi. the parent series can be transformed into a hyperbolic function and make x =pi you have a series wit only algebraic numbers that gives you e^pi. I couldn't do it though but I think if someone smarter put more effort in they could do it.
>>7640773
Yep, I'm just ignoring your comment on gamma functions and charging ahead to amuse myself (and by way of my suggested above comparison).
Here is a BADLY SKETCHED NOT-DONE CONCEPT (we have a blackboard here on which to write:
[math] \displaystyle \phi = 2^{3/5} \sum_{k=1}^{ \infty } \frac{ (-1)^{k??} 4 \prod\limits_{j=0}^{???} (5j+1)(5(j+1)+1)}{5^{2k} \; 2k!} [/math]
This does not account for the leading term of unity, and I haven't even really checked the bits for accuracy, but the product's indices should key off of the outer series' index.
>>7640774
Thanks, that's very nice of you. What about mechanical engineering? I'd consider that. I like to make things.
>>7640795
That kind of definition works, it was the one I used initially but it's a bit inelegant. Trust me gamma function is the way to go. The problem was that the gamma function part was the bit I had taught myself so when I converted that to the gamma function definition I didn't really know what the fuck I was doing but it werked however I don't remember it at all.
>>7640434
On the contrary OP, while Wikipedia and Wolfram Mathworld may not list them explicitly, series and sequences for the golden ratio are quite numerous and well-known. Two more series involving the golden ratio are [eqn]\sum_{n=1}^\infty \frac{\zeta(2n)}{n100^n} = \log \frac{\pi \varphi}{5}[/eqn] and [eqn]\sum_{n=0}^\infty \frac{1}{F_{2^n}} = 3 - \varphi [/eqn] where [math]\zeta(s)[/math] is the Riemann zeta function and [math]F_s[/math] is the sth Fibonacci number. Here is an example of a product [eqn] \prod_{n=1}^\infty \left( 1 + \frac{F_s}{F_{2^n r + s}} \right) = \frac{\varphi^{2r} - (- \varphi^{-2})^s}{\varphi^{2r} - 1}[/eqn] Setting r = s = 1 gives the special case on Sondow's page here.
>>7640778
>>7640797
ofc, anything where advanced maths are used. EE, chem E, mech e, all dank. you're sure to be a success if you maintain this quality of work.
>>7640825
Liking the one with the zeta function, any link to the proof?
>Wikipedia and Wolfram Mathworld may not list them explicitly
I'm virtually an amateur hence why I skimmed these two sites and assumed they weren't any. Sorry that I was wrong.
>>7640838
1: The zeta function one follows from the following expression [eqn]\pi x \cot (\pi x) = 1 - 2\sum_{n=1}^\infty \zeta(2n)x^{2n}[/eqn]Dividing through by x and then integrating the resulting expression gives [eqn]\log (\sin(\pi x)) + C = \log(x) - \sum_{n=1}^\infty \zeta(2n)\frac{x^{2n}}{n}[/eqn]where C is then shown to be [math]-\log \pi[/math] by taking the limit of the expression as [math]x \rightarrow 0[/math]. The desired identity follows by setting x = 1/10.
2: The aforementioned cotangent expression is a relatively well-known one. We may show it as a consequence of Euler's product formula for [math]\sin x[/math] [eqn]\frac{\sin(\pi x)}{\pi x} = \prod_{r=1}^\infty \left(1 - \frac{x^2}{r^2} \right)[/eqn]Take logarithms on both sides and differenate with respect to x. Then after a bit of rearrangement we have
[eqn]\pi x \cot (\pi x) = 1 - 2 \sum_{r=1}^\infty \frac{x^2/r^2}{1 - x^2/r^2} = 1 - 2\sum_{r=1}^\infty \sum_{n=1}^\infty \left(\frac{x^2}{r^2} \right)^n = 1 - 2\sum_{n=1}^\infty \zeta(2n) x^{2n} [/eqn]
>>7640984
>I namedrop Jon Sondow to OP despite knowing nothing about him except mathworld associations, taper off bothering to rephrase OP's expression, and am rewarded by an acknowledgement of the link and witnessing a further post dashing off more exquisite pearls like they're nothing courtesy a third party
Very nice, you humble me. Er, I fail to see whither phi in all this. Specifically, presumably phi's place in the former expression of >>7640825 is the result of a happy plug-in in either the latter or perhaps second expression in >>7640984 ...
>>7640542
Because it's a kinda boring analytic result.
thread is giving me flashbacks to that topics course I took on analytic number theory and it's a mixed bag of feels.
>asking a Burmese cattle herding board whether or not to publish something
kek
>>7640473
>You can't publish it without a proof. Also you spend way too much time on such a shitty board.
the proof is left to the reader and this is quite known
>>7641296
kek
>>7641018
>It's not P=NP
>It's not ABC conjecture
>It's boring
Sure is pop-sci in here
>>7640473
>irregardless
Still, publish proof
>>7640434
Upload it to viXra I'm sure they'll take your contribution to the field.
>>7641863
>these assumptions
>>7641863
It's boring. What do you want me to say? It's a numerical identity, and it has little impact on other fields of mathematics. Be realistic.
>>7641977
But it's math. /sci/ is as bad as all the pop-sci channels it hates. Anything that's real and within their knowledge level is seen as too boring for them. If you find OP's identity to be boring then you shouldn't be on a math board honestly. Infinite series are cool as fuck.
>>7641996
I'm studying other fields of math that are objectively more interesting, in that they are the amalgam of work in many fields and affect many fields. Why are you baselessly claiming that I don't belong on this board? I consider that a case of bad reasoning.
>>7641996
So we should discuss trig identities as well then? Just because it's math doesn't make it interesting, worth discussing, or of any consequence. I get that this guy is excited that he found something, but there's nothing to discuss beyond saying "hey I found this neat little expression for a number."
>>7642220
I should have mentioned that what would be particularly interesting would be the proof, but by OP's admission it is straightforward and nothing new. If there is nothing creative being done, I don't see what differentiates this from discussing Calc 2 problems.
>>7641863
What do you study, and on which level? Already after two years in uni, I had had more than my voluntary share of analysis. Call it le algebraic topology meme xD or what ever you want to, but this kind of stuff just keeps my dick flacid. Logic makes me breath more heavily, algebra makes my dick pulsate, but alg top makes me cum.
Of course, I congratulate OP for his result (assuming it is correct, and more if it is something new). It is just not interesting enough for me to actually spend time thinking about it.
>>7642220
Am I reading this right? Is an anon really sperging out over the fact that someone wants to discuss math on the math board? I was under the impression that all math was up for discussion here not what the high priests of /sci/ decides tickles their autism on that particular day
>>7642809
I think I did a poor job explaining my position. We should absolutely discuss math on the math board -- in fact, that's what all threads should be on. However, the converse doesn't hold; just because a post is about math doesn't mean that it needs to be discussed or is a good post.
Not even to say that this is a bad post, but OP is angry that nobody is interested in his thread. This is because different people have different interests. Your average algebraist may not have any interest in discussing an analytic identity for the golden ratio. As a matter of fact, OP's post had no intent of actually discussing the identity or why it's true. He just wants to know if he should publish. If he wants to discuss the proof, that's great, but by his own admittance the proof is uninteresting. These sorts of things are basically trivia facts if the proof has no new ideas.
>>7644025
exactly. OP is hoarding the proof and getting mad when nobody discusses it. If you find it uninteresting and don't want to publish it, at least tell us what the fuck the series is. You don't even have to give a proof just try to explain it a little and get the discussion started.
>>7641018
Oh sorry it's not about birational quaternionic extensions of anti-topological C_infty[X1,X2,...] spaces over infinite dimensional categorical nigger fuckers
>>7642027
>I'm studying other fields of math that are objectively more interesting
You're objectively retarded
>>7644046
Allow me to paint a scenario:
>anon starts a thread on neat tricks for multiplying integers
>other anon says that it's boring because there are more interesting things to discuss
>second anon explains that discussing broader topics is best because they affect more fields, and thus more people can contribute to discussion, and also because the discussion won't pertain to something that can be verified by a computer algebra system
>first anon slings shit at second one because he wants to talk about multiplying fucking integers
Who /really/ looks like the baboon? Get off my board, it's starting to smell icky.
>>7644049
Please, do explain. I am retarded because I made a factual claim that follows from the definition I gave in this post [>>7642027]? Stop being ignorant. You aren't /actually/ defending a math thread, because all of the good math threads started on this board (whether by me or by the other resident mathematicians) get pruned because nobody posts in them. Do you see why it is hard for me to stand by and see a kinda lame thread get bolstered AND defended for being one if the "rare math threads?" This is absurd.
Numerator still missing
8^(1/5) * ((-1)^n) (1+(sum from n to inf ( (?????) / (5^(2n)*2n!) )))
[math]
\sqrt[5]{8} (-1)^{n} (1+ \sum_{n=1}^{\infty} \frac{????}{5^{2n} \times 2n!})
[/math]
?????(n=1) = 4
?????(n=2) = 4*6*11
?????(n=3) = 4*6*11*16*21
?????(n=4) = 4*6*11*16*21*26*31
?????(n=5) = 4*6*11*16*21*26*31*36*41
Any ideas how to write this?
>>7644120
>My board! I belong here! See, here's my credentials, my identity! Notice me! People who I don't like get out of my board! My threads are good :^)
namefags are the fucking absolute worst, stop being an attention whore, faggot. "it's kinda boring" is not a reason for anything, especially not for a stupid cunt trying to police an anonymous imageboard. your only quip here is that you're mad people are having fun without you, and that's retarded because WE'RE FUCKING ANONYMOUS HERE, this is NOT your private club
>>7644152
I have no problem with this thread. Have fun, I don't give a shit. But you are a hypocrite: I can't be "possessive" over the posts - and quality thereof - on this board, and yet YOU are the one saying I can't come into your thread and express an opinion. Who again is the megalomaniac here?
You need to just grow up and learn to argue. I am making a damn good point, and you won't argue your side because either (a) you have no argument, or (b) you don't know how to present a formal argument. All you did was make fun of me (on an anonymous Finnish boot-shining bulletin), and the person people are going to listen to is the one presenting solid points. So keep spewing hot air and spittle, big guy.
>>7644120
>because all of the good math threads started on this board (whether by me or by the other resident mathematicians) get pruned because nobody posts in them.
wowee zowee fuckboy. looks like your jimmies are rustled because people like number theory instead of whatever the fuck you study. go post content instead of bitching.
>>7644173
>your thread
??? never told you to get out, just that you're tremendously retarded for policing shit, which you are
>im making a damn good point
>"This is boring, stop discussing it"
>good point
10/10 would get baited by namefags all day long
either way I don't have a side here, all I came to say is >>7644152, you can have fun arguing about shit with the other dudes and helping everyone else confirm that namefags are the absolute worst kind of retard. you're delusional if you think you're presenting "solid points", if you actually stopped caring so much about your fucking identity and image you'd maybe be a little less shitty.
>>7644174
Nobody is discussing number theory in this thread. OP just keeps saying
>look at my identity
>isn't it pretty?
>should I publish?
The final equation doesn't matter. The math is in where it comes from and why it's true, but nobody is discussing that anyways.
>>7644184
OP here, the guys arguing are not me, im not mad who says i am mad? this thread got 60 replies on a slow board and my question WAS answered.
ok so i skimmed through this and it seems the flame war is caused by people saying this is getting less replies than the meme threads just because its "dull" number theory but the othrr side has a point too because i never posted the proof so theres nothing to discuss. Therefore ill post the proof and see what happens.
Goddam newfags don't know old meme thread
>>7644144
When you can't find how the hell an equation with multiplication works, always try to reduce every number to primes multiplications.
But that doesn't work here, but here you can see a pattern (if you ignore the 4): (6+10n) and (1+10n).
Now that you have the pattern, just multiply everything altogether and you get: 4*(Multiplication from k=o to n of)(6+10n)(1+10n)
