#Is it possible to find a function that behaves exacly like this graph?
518 messages · Page 1 of 1 (latest)
Ohh i Will try
gl
closest ive been: ln(x)/(sin(x))
,w plot ln(x)/sin(x) from x=-2 to x=100
Not baadd
Okay it’s not the one you’re looking for but i find it beautiful
but you know
I gave its roots, max local point and the point where it actually starts decreasing all the way to -infinity
I was thinking it might help
That would help a lot
yeah
here it is again
all roots are of the form npi where n is an integer ofc
then the max local idk
What I’ve seen is that it intercepts the x axis every pi
yes
exacly
since as x->npi then f(x) -> infinity
thats why the closest ive come is ln(x)/(sinx)
where ln(x) comes from the tail of the function
It cant be divided by sin(x)
Your graph is continuous
?
I mean the curve can be drawn without leaving any gaps. Just like 1/x is not continuous
If sin(x) is in denominator and that x=2pi or 2kpi then it’s not continuous
You will have something divided by 0
But in your graph there are no gaps
k
But your right about considering sin though
Maybe even ln(x)
But sin is definitely not is denominator
ln(x) can’t be there either because at x=0 there is a defined value in your graph
but we can do ln(x+a)
Yeah that
but again if we inster -a we would get a singularity
Wait it can’t be that either
yh
Just keep sin
Do you have a wider view?
DANGG
not continuous (obviously)
It is continuous because i see no gaps, do you see some?
yes
Where
What is going on here
No it just oscillates
k
👀
point is
can we get a function out of this graph
for now the most suiteable is somewhere around (lnx)/(sinx)
even tho its not even close
im sped srry
but yh
What I also did was trying to make a infinite product series expansion
since we have npi
also dint quite work either until I got this
that was the same product infinite series expansion but with some modifications
kinda used Euler's method for that
but still wasnt what I was looking for
Where did you get this graph from
the infinite product series I made
but it isnt a full closed in function
are the gaps due to asymptotes, or are they due to a curve that has an extremely high max/low min
I don’t think you would need to go that far but i honestly don’t know either.. Also i noticed that starting from x=8 approximately, the function “jumps” very high
asymptotes but you start with low and mid
¯_(ツ)_/¯
,w plot sin(x)tan(x) from x=-3 to x=100
Nah it’s bad
,w plot 2^xsin(x)
Is it continuous
try desmos
Well it looks like it is
it is
,w plot 2^xsin(x) from x=-10 to x=100
close
OHHHH
What if those are asymptotes
,w plot 2^xsin(x) from x=-10 to x=10
i mean you can piecewise
I think these are very high oscillations. Like so high you can almost say they are asymptotes
yh
does wolfram supports piecewise?
idk
,w plot (-2)^xsin(x)
,w plot (2^x)sin(x)tan(x) from x=50 to x=70
,w plot \begin{cases} x&x>0\0&x<0\10&x=0\end{cases}
not even close😭 🙏
CASE COUNT LETS GOOO
$\begin{cases} x&x>0\0&x<0\10&x=0\end{cases}
$
Tangent
Compile Error! Click the
reaction for more information.
(You may edit your message to recompile.)
oops
yh
$\begin{cases} x&x>0\0&x<0\10&x=0\end{cases}$
Tangent
not bad
whats case count?
No idea lol
its better
,w plot (2^x)xsin(x) from x=-3 to x=30
I just copied lol
let me copy and see on desmos rq
beautiful
It looks air turbulence
yes it does
I dont think thats even close but I guess
does this count?
Let me try a function
but i was finding it when yall were doubg your first attempts
So close
,w plot 2x
I got the best one
yes very close
real
THIS SHIT IS PEAK 🔥🔥
Thank you thank you
I checked and the beginning of the graph doesnt really quite match but with some coefficients here and there it probably would end up matching
yeah
also doesnt have to be a variant of -x^2, thats just the first thing i thought of
also you did set up boundaries /:
wait i have an idea
Never thought i would have some pleasure finding functions lol
without piecewise
go ahead
this is what makes us nerds~
we dont look to heaven and we put math first~
Its not fun to me tbh /: Im doing this for a reason actually
Not even the tiniest slightest bit..?
not rlly...
Dang…
bros locked in
appart from being closer to my goal then I was before
you sound like a very math-oriented anime villain
ye
W math
im obsessed
okay lets see here
so basically a math-oriented anime villain
^^^
sure I guess
Ever since you came up with 2^xsin(x) this all got easier
also
yes i saw this in a "desmos music" video today and i immediately thought it is kinda matching
this was extremely fun
?
😭
desmos music video im crying
comparison between graph and your function
OMGGG
send me the original
k
x\prod_{n=1}^{100}\left(1-\frac{x^{3}}{n^{3}\pi^{3}}\right)
but its an infinite product
thats what I hate
bestie chill
and thats why I came here
uh oh where do you graph it
desmos
what since when desmos has $\prod$
Tangent
yoooo
bro
just go on desmos
and write the following
prod
boom
here it is
anyways
dunno
or just look up I guess
I have a course in like 20 minutes so Ill leave and you guys can keep trying and compare with the real graph if you want. Ill come back in around 3 hours or so
gl
kk bye man
thats betetr
how are you doing this you absolute whiz
i got better
$\frac {2^x\sin x\left(\frac {|x-\pi|+x-\pi} {15} + 1\right)} {e\left(\frac {|x-\pi|+x-\pi + 1} {2} + 1\right)}+\frac{|x|(-x^2)} 5+\frac{x^3}5$
Tangent
lemme try lmao
nice👍 Maybe try a bit more until it matches perfectly. Ill test this function on my side.
god dayum
$y=(2^xsin(x)((abs(x-pi)+x-pi)/12+1))/(2.718281828*((abs(x-pi)+x-pi)/2+1))-(abs(x)*x^2)/6+x^3/6$
V
nice!
Now can you guys measure the error between the starting function and the one you found??
i have been working on nimbus ( google cloud from past 5 hours almost) and well finialsed it rn, its just storing up
oh nice!
well hope its going well
no pressure
as under my own perspective, the starting fucntion is controlled
but yea i'll be writing aa long asss shiitt for explanation i can feel. already on it tho. can say 13% done
omg its you- bro did so much calculus and graph modelling that bro forgot basic arithmetic 😭💔 i get it tho
mother fuckaaa
i got it
*The starting function is
f(x) = x ∏ from n = 1 to 100 of (1 − x^3 / (n^3 pi^3))
This function is a finite Weierstrass-type product. Its structure is completely determined by its zeros and by polynomial growth.
First, the zeros.
The factor x forces a zero at x = 0.
Each factor (1 − x^3 / (n^3 pi^3)) becomes zero when x = n pi.
Therefore, the function has zeros at x = 0, pi, 2pi, 3pi, … , 100pi.
These zeros are polynomial in nature. Near x = n pi, the function behaves like a linear factor multiplied by many nonzero constants. This gives smooth, flat crossings of the x-axis with no sharp cusps or switching behavior.
Second, smoothness.
The product consists only of polynomials. Therefore f(x) is smooth and differentiable everywhere. There are no absolute values, no exponential switches, and no artificial cutoffs. Every change in the graph is dictated by algebraic structure alone.
Third, growth behavior.
Each factor contributes a cubic term in x for large x. Since there are 100 such factors and an additional x in front, the overall growth of f(x) behaves like x to the power 301. This means the function grows polynomially, not exponentially.
The constructed function is
g(x) = (2^x sin(x) times a switching factor) divided by a constant, minus a polynomial correction term.
This function is not a product approximation. It is a curve-fitting construction.
First, zeros.
The sin(x) term forces zeros at x = n pi for all integers n, not just up to 100. These zeros are trigonometric in origin, not algebraic. Near each zero, sin(x) crosses the axis linearly, which is a different local behavior than the polynomial factors in the original product.
Second, growth behavior.
The dominant term in g(x) is 2^x. This introduces exponential growth. Exponential growth cannot approximate polynomial growth over large intervals. Even if the graphs look similar in a small window, they diverge rapidly as x increases.
Third, switching terms.
The absolute value expressions introduce piecewise behavior. This creates nondifferentiable points where the original function is perfectly smooth. These switches do not exist in the product and therefore introduce structural error.
Fourth, artificial damping.
The polynomial subtraction terms are used to suppress unwanted growth on one side of the graph. This is not derived from the original product but is added by hand to force visual similarity.
The error between the two functions can be understood conceptually as follows.
Near x = 0, the two functions can be made to look similar because both behave like low-degree polynomials.
Near x = n pi, the zero locations match, but the local shape does not. The original function has algebraic zeros coming from product factors, while the constructed function has trigonometric zeros from sin(x). This creates noticeable local curvature differences.
For larger x, the error grows rapidly because the original function grows like a high-degree polynomial, while the constructed function grows exponentially. No choice of constants can reconcile this difference globally.
Conclusion would be that -
The starting function is a structurally defined algebraic object whose behavior is dictated by a finite product and polynomial growth.
The constructed function is a visually motivated imitation that matches some qualitative features, such as zero locations and spike placement, but does not preserve the underlying mathematical structure.
Therefore, the difference between them is not a small numerical error but a fundamental theoretical mismatch in growth order, smoothness, and functional origin.*
@everyone
@slow marsh @wicked crest @tepid fiber
turu
my hands lmao
typing all this
im gonna rest now
u read it
ill be reading it later because I have a tutorial to attend to but honestly this deserves a round of applause
👏
👏👏
thanks bud, anything for math
but why aint these peeps approving my graduation + role
ouchie
same here
¯_(ツ)_/¯
ok
bro u got contact with admin or mod
duh i need my graduation + role
lmao
i mean post graduate

no. I tend to work alone on a white board then spending time in this math server. I only come to give side problems when they come as an obstacle in my mathematic research
i was bored tbh so thought why not give out my PhD knowledge
lemao
make sense
i mean, being senior developer alot of things are on ur shoulders, and i needed a brain teaser for myself
of course
so what u do?
Wth
You guys are still on this ??
until we die, we always on smth
i get horny studying maths or physics

these are my turn on
basically a guy named Euler one day said to himself "Why cant I just factor sin(x) as a infinite polynomial" and so he did. Then, he proceeded to ask what would happen if we de-factorized the infinite product series he built and that reveald to him something interresting because the second term of the original taylor series of sin(x) which is -(x^3)/3! but then when expanding the infinite product series we instead get (when tracking all that has x^3): -x^3 (1/(pi^3) + 1/(2^2 pi^2) + 1/(3^2 pi^2) + ...). Logical thing he did: Since it will eventually make the -(x^3)/3! term he set them equal on both sides: -(x^3)/3! = -x^3 (1/(pi^3) + 1/(2^2 pi^2) + 1/(3^2 pi^2) + ...) and later found out that eventually (pi^2)/3! = 1 + 1/2^2 + 1/3^2 + ... = zeta(2) therefore claiming that zeta(2) = (pi^2)/6.
Here its quite similar but the starting point is another infinite product series
in this case that one:
mhm...
here if we are able to find a function that is related to this infinite product series then its bingo since we also have its taylor series
and thanks to you
I also found the following equality
ayy no worries, my pleasure
zeta(3) = (theta)(pi^3)/4! where theta ~= 0.930436310465
try it out if you dont believe me
god dayum, im hard
did u take phd degree

..
im pursuing it right now
ill comeback in 2 hours lecture starting now
can say, im finished, its my final year, practicals right now and then final exams
and im finished
slay
i would have studied enough to like be that cool guy in society, and will continue my own reasearch after it
like im a CSE major
What’s CSE?
but, maths is love lmao
computer science engineering
Dangggg okayy
same but still didnt really major in it yet
since im a first year
in simple words, im programmer
print(“hello world”)
print("hello world")
print("functions have inputs")
print("changing the input changes the function")
god somebody kick my ass
there's this guy in #1464335239672500507
god
Import numpy as np
A=np.array([1],[2],[3])
B=np.array([4],[5],[6])
t=np.dot(A, B)
print(t)
32
Wait I’m coming
oh my baby
"a guy named euler" lol
soooo need help lmao
@tepid fiber
Bro. You're a graphing genius!
ty ig
I'm just impressed.
bro himself is a tangent
His powers were given to at birth.
Your proof was awesome too, ngl.
I'm a nerd.
I read mathematical proofs for entertainment. Lol.
i get horny seeing them

Ooh.
I'm flattered.
That hypothesis is a fascinating one.
Ayyyyyy me too.
lol
yeah
"the music of prime numbers" by marcus du sautoy
recommended although he started saying stuff aboit physics that i dont like
I thought you were gonna say politics. Lol.
Let's keep those out of here.
I'll have to check that out.
wanna here smth guys?
broo i have been up soo muh
i can see my text going into fourth dimension
ok
Physicists eh?
yuck
What? I am interested?
Oh. Isl see.
This looks like calculus until you write it down carefully, then it turns into analysis, then functional analysis, then probability, then you realize it was information theory the whole time and the problem was never about numbers, it was about you.
They're like mathematicians with more formulas, and less "mystery solving" type math.
HA!
Alr.
I try to break you for entertainment. Lol. And sometimes it even works.😭 🙏
for more context, your name is zeta yk zeta function haha get it? 
wow, is this how mathematicians flirt? making bad math-puns to each other? because if so, get a damn room
Get out if the discord server named "mathematics" if you don't like it.
What!?
Impossible.
Tell me your findings!
Not literally XD. For example: zeta(3) = (sigma)(pi^3)/4! where sigma = - (d^4)/(dx^4) (x product(k>1) (1 - (x^3)/(k^3 pi^3)))|(x=0) ~= 0.930435923838 and normally we want a clean (pi^3)/4! so then to find the missing percentage we do (1 - sigma)(100) ~= 7% so we are missing zeta(3) by just 7%. Crazy right?
ayoo gois wassup
But the general formula should be zeta(s) = -(pi^s)/(s+1)! (d^(s+1))/(dx^(s+1)) (x product(k>1) (1 - (x^s)/(k^s pi^s)))|(x=0)
yooooooooooooo
oh wait smth serious is goin
@idle ginkgo @tepid fiber @tacit furnace ayo guys
i bought a new superbike, 4th in my collection
i never stated that i wasnt one of them ;)
yoo proof lover
You know way more about this than I do, lol.
You deserve the title zeta.
Niceee.
aghh yestarday was her first wash
cuz it rained here
its the aprilla rsv4
That's gonna be sick!
waddupp zetaa
I guess… but it’s not enough tbh. That’s why I’m now trying to find the multiplication of multiple converging functions that is equal to the infinite product of 1 - (x^3)/(k^3 pi^3). This will allow (if found) to find the full Taylor series of that function which would help defining sigma as a combination of transcendentals and fractions/irrationals since Apéry never mentioned that zeta(3) !=?/? + ?/? if yk what I mean… he only said that zeta(3) !=(pi^n)/a where a is a number and n also.
I'd like to get on this train, ngl.
Ima go watch some videos, and read some papers.
I don't completely understand what you're saying, but I want to learn!
ay ping me what's the prob im bored rn
Find a closed form for x product(k>1) (1 - (x^3)/(k^3 pi^3)) = ? Just like how for example x product(k>1) (1 - (x^4)/(k^4 pi^4)) = sin(x)sinh(x)/x
mhmmmm less seee
If you find such function it will simplify my life
roughed out like 4 papers rn
Damn
I already used 10 chalkboards to find a closed form expression and got really close to find one
aghhhhhhhhhhhhhhhh
i might have gott itt
MIGHTT
but i would say one thing
**There is no elementary closed form like
sin(x)sinh(x)/x
for the product
product over k>=1 of (1 - x^3/(k^3 pi^3))
The reason is that this product has three sets of zeros (coming from cube roots of unity), unlike the x^4 case which splits nicely into sin and sinh.
The best possible closed form is in terms of Gamma functions:
product over k>=1 of (1 - x^3/(k^3 pi^3))
= C / [ Gamma(1 - x/pi) * Gamma(1 - omega x/pi) * Gamma(1 - omega^2 x/pi) ]
where
omega = exp(2 pi i / 3)
and C is a constant (can be fixed by normalization).
So the conclusion, in one line:
There is no representation using only sin, cos, sinh, etc.
The natural closed form lives in Gamma / Barnes type functions.**
$prod_{k>=1} ( 1 - x^3/(k^3*pi^3) )
= S_3( x/pi | 1,1,1 )$
V
$S_3(z | 1,1,1)
= prod_{n1,n2,n3 >= 0}
( n1 + n2 + n3 + z )
/ ( n1 + n2 + n3 + 3 - z )S_3(z | 1,1,1)
= prod_{n1,n2,n3 >= 0}
( n1 + n2 + n3 + z )
/ ( n1 + n2 + n3 + 3 - z )$
V
thank you ;)
wow i understand none of this but my love for yall has increased exponentially
wait i js realised
the mathematics servers gif is the rainbow pride flag and trans flag
ohh
yo guys i was working out on relativity theory and i came across a theory of my own
@tepid fiber u think that the universe is observer dependent?
@slow marsh @wicked crest @tacit furnace my bad for mass tags but its just going over my head i hope you get me
no. Universe is universe and universe is not unique for each individuals. Unless... Yk they have certain condition then the universe would look different to them but in general the universe is one thing that doesnt differ. Always chaotic too btw.
bro but If two observers can record different times and lengths for the same event, then reality itself is observer dependent, not fixed.
and doesnt it challenges newtonian ideas?
Time flows the same everywhere
Space is rigid and absolute
these ideas
what do u say
its not a bad idea tbh
yea that's what im sayinggg
ayoo wake these nuggas up
lets hit vc

im having a rot

💀
i love this guy
yk 9/11 was to cover up the mestirious money that vanished from the government and a excuse to go to iraq to get oil
just cool fun fact nothing personal
😭 🙏
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hey twitch
Relativity does not merely revise measurements of space and time,
it destroys the existence of a global, observer-independent temporal order.
and if that happens then
Time is not an intrinsic feature of the universe.
Space & time does not exist as a fixed container.
Reality is relational, defined only through physical interactions.
btw this guy just planned this. he didnt fly in the plane, and also the plane didnt just drop a bomb it FLEW RIGHT IN THE TOWER
ayyy its just jokes

