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/sci/ - Science & Math

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7138076 No.7138076 [Reply] [Original]

what's your favorite function?

>> No.7138079

e^(iπ) + 1 = 0

It's beautiful.

>> No.7138107

>>7138079
>function

>> No.7138274

>>7138076
>your favorite function?
Heaviside Step

>> No.7138304

>>7138076
Laplace transform.

>> No.7138323

>>7138076
f(x) = 5

>> No.7138325

>>7138076
Dirac's delta :^)

>> No.7138346

arctan(x)

>> No.7138355
File: 339 KB, 680x680, 461.png [View same] [iqdb] [saucenao] [google]
7138355

>>7138325
>BUT IT'S A DISTRIBUTION
>REEEEEEEEEEEEEEEEEEEEE

It's gotta be the exponential function for me, so useful.

>> No.7138359
File: 2 KB, 182x46, function.png [View same] [iqdb] [saucenao] [google]
7138359

This one.

>> No.7138398

>>7138359
that's a relation, not a function

>> No.7138409

>>7138398
post a pic faggot

>> No.7138415

>>7138409
huh? http://www.wolframalpha.com/input/?i=x%5E2%2B%28y-cuberoot%28x%5E2%29%29%5E2+%3D+1

>> No.7138419

>>7138076
The spherical harmonics.

>> No.7138430

conjunction junction!

>> No.7138445

>>7138415
doesn't look like a relation to me

but that's also not what the dude posted so maybe you want this
http://www.wolframalpha.com/input/?i=x^2++y-cuberoot+x^2++^2++%3D+1

which also doesn't look like a relation

>> No.7138495

the function of all functions

>> No.7138496

>>7138409
http://www.wolframalpha.com/input/?i=x^2+%2B+%28y-cuberoot%28x^2%29%29^2%3D1

>> No.7138499
File: 11 KB, 800x216, EulerIdentity1.png [View same] [iqdb] [saucenao] [google]
7138499

I like this one.

>> No.7138502

>>7138076
Fourier transform bitches!

>> No.7138508

>>7138419
B A S E D L A P L A C E
A
S
E
D

L
A
P
L
A
C
E

>> No.7138538
File: 481 B, 63x21, ce18201395abe945ab4883979db279f0.png [View same] [iqdb] [saucenao] [google]
7138538

>>7138076
wave function

>> No.7138561

>>7138499
That's an identity anon. The filename literally says it.

>> No.7138563

>>7138076
Trace

>> No.7138565

I like Euler's Gamma function; so useful in so many ares of complex analysis, as well as combinatorics and theoretical physics.

>> No.7138582

I really really like this one
1+1=2

>> No.7138584

weierstrass function

>> No.7138594

>>7138561
Whats the difference?

>> No.7138611

>>7138594
A function is a set of lists of two values such that if the first values of two objects are the same, the second values of the objects are the same

>> No.7138631

http://en.m.wikipedia.org/wiki/Busy_beaver

Stay computable, plebs.

>> No.7138639

>>7138079
>imaginary pi
Wot

>> No.7138643

>>7138639
go to class m8

>> No.7138647

>>7138631
my favorite function is the indicator function of the set of theorems of true arithmetic

stay zero-jump computable u lil bitch

>> No.7138727

Id

>> No.7138751

My favorite one is arccos(x)-xsqrt(1-x^2)=(3pi)/8

;o)

>> No.7138754

>>7138727
The one true answer.

>> No.7138768

Is it possible for a function to exist which contains all finitely bounded functions (shifted obviously)?

>> No.7138774

>>7138768
You might find this interesting:
http://en.wikipedia.org/wiki/Zeta_function_universality

>> No.7138775

>>7138774
Cool.

>> No.7138802
File: 2.55 MB, 1881x2821, locally_grown.jpg [View same] [iqdb] [saucenao] [google]
7138802

>>7138768
A "natural" one with many parameters is the Meijer G-function.
There is a the Fox H-function, which I think is a generalization.

http://en.wikipedia.org/wiki/Meijer_G-function#Representation_of_other_functions_in_terms_of_the_G-function

Regarding the thread, one of my favorite is the Mittag-Leffler function
http://en.wikipedia.org/wiki/Mittag-Leffler_function
because it interpolates between some common relevant functions with few parameters.

I like the matrix elements of the Wigner-D matrix, because, morally, they are a reason for a lot of the special functions in physics:
http://en.wikipedia.org/wiki/Wigner_D-matrix

I also like

<span class="math">\frac{1}{1+x^2}[/spoiler]

>> No.7138806

>y=x
very easy, obviously the best function

>> No.7138809

>>7138802
many upboats to you Emmabro

>> No.7138810

>>7138806
that's a relation between two variables

>> No.7138814

>>7138810
I think he means Id(x).

>> No.7138825

KEEP DANCING WITH YOUR FAERIES; FUNCTIONS ARE FLAWED

https://www.youtube.com/watch?v=_6B2PUn99Bc

>> No.7138835
File: 275 KB, 800x483, faries.jpg [View same] [iqdb] [saucenao] [google]
7138835

>>7138825
>KEEP DANCING WITH YOUR FAERIES

>> No.7138840
File: 156 KB, 549x349, MathematiciansHateHim.png [View same] [iqdb] [saucenao] [google]
7138840

>>7138825

>> No.7138847

>>7138825
>babbies first constructivism
>he acts like this is ground-breaking stuff
and judging by that nearprime function I'm guessing he's an ultrafinitist as well

>> No.7138867
File: 3 KB, 97x114, Weierstrass_p.svg.png [View same] [iqdb] [saucenao] [google]
7138867

weirstrass' p function is breddy gud

>> No.7138868

>>7138847
>he acts like this is ground-breaking stuff
wat.
I don't think he's ever implied that.

>> No.7139470

The Weierstrass function is a function which is continuous, smooth, and not differentiable at any point.

>> No.7139484

>>7139470
I'm intrigued. How?

>> No.7139490
File: 60 KB, 795x505, 795px-WeierstrassFunction.svg.png [View same] [iqdb] [saucenao] [google]
7139490

>>7139484

>> No.7139716

>>7138825
NJW is a genius, but he's like a mathematics /mu/sician. he uses a nonstandard framework simply because the the standard framework is used by everyone and is thus shitty and flawed.
we need people like him in physics research.

>> No.7139727

>>7138825
does he have schizophrenia? his speech pattern is quite strange, and there are a bunch of unnecessary jump cuts. he also just 'looks' like he has schizophrenia (in his eyes).

>> No.7139730

>>7139727
How do you get schizophrenia in your eyes?

>> No.7139747

>>7139716
Basically you are saying that he's a contrarian concerning mathematics. But this is why he is popular here, because this is nothing else than a site for contrariens.

>> No.7139752
File: 2 KB, 260x49, fb535a294859013f7d6b2c4e9bec21f3.png [View same] [iqdb] [saucenao] [google]
7139752

>>7138076
The hypergeometric function.

>> No.7139769

>>7139752
Could someone explain the hypergeometric function and its significance?

>> No.7139825

>>7139769
It provides solutions to the hypergeometric differential equation.
Kind of like Bessel functions when a DE is in the form of Bessel's equation.

>http://mathworld.wolfram.com/HypergeometricDifferentialEquation.html

For applications, I've come across it in astrophysics when solving for gravitational potential along with the Gamma function and Meijer G which appear reasonably frequently.
Someone else here should be able to give a much better description of its significance.

>> No.7140384
File: 154 KB, 970x779, emma-jaoquin-woody-14jul14-01.jpg [View same] [iqdb] [saucenao] [google]
7140384

>>7139769
>Could someone explain the hypergeometric function and its significance?

Say you have to solve the differential equation <span class="math">f’(x)=f(x)[/spoiler] with <span class="math">f(0)=1[/spoiler].
You naturally make the ansatz

<span class="math">f(x) = 1+\sum_{n=1}^n c_ x^n = 1 + c_1\, x + c_2\, x^2 + c_3\, x^3 + …[/spoiler].

so that

<span class="math">f’(x) = c_1 + 2c_2\, x + 3c_3\, x^2 + [/spoiler]

Comparing coefficients, this implies that the solution to <span class="math">f’(x)=f(x)[/spoiler] must have, for example <span class="math">3c_3=c_2[/spoiler]. In fact all coefficients are determined this way, by the recursive relation

<span class="math">c_{n+1}\, /\, c_n = 1\, /\, (n+1)[/spoiler]

With the polynomial <span class="math">q(n) := n+1[/spoiler]. This means

<span class="math">c_n = = \frac{1}{\prod_{k=1}^n q(k)} c_0 = 1/n![/spoiler]

and hence

<span class="math">f(x) = 1+\sum_{k=1}^n (1/n!) x^n [/spoiler],

which is the exponential function (duh).

Such an approach to solve a differential equation will often look like this. Consider the majority of functions in this thread. They have series coefficients <span class="math">c_n[/spoiler], such that

<span class="math">c_{n+1}\, /\, c_n = p(n)\, /\, q(n)[/spoiler]

where p and q are some polynomials.
Now any (arbitrary product of) polynomials in n can be written as a product of terms <span class="math">(a_i-n)[/spoiler].
So define the general hypergeometric function

<span class="math">{}_pF_q[a_1,…,a_p; b_1,…,b_q](x) :=[/spoiler]

<span class="math">=1 + (a_1 … a_p)\, /\, (b_1 … b_q) x + (a_1 (a_1+1)…a_p (a_p+1))\, /\, (b_1 (b_1+1)… b_q (b_q+1)) x^2/2+…[/spoiler]

to catch them all!

They are the solutions to differential equations with recursive character.

>> No.7140556

>>7138445
Lrn2relation

>> No.7140846

fag(x) return 1 -> x is a fag and 0 otherwise

example:

fag(OP) return 1

>> No.7140903

>>7139490
Oh, it's fractal. Neat.

>> No.7140913

>>7140903
It's all corners, at every point.

>> No.7141296

>>7140913
If it's all cusps, then it can't really be called smooth, can it?

>> No.7141573

>>7138076
Conjunction

>> No.7141579

>>7139747
No it's not everyone here is conformist as fuck. Anyone here would agree with me.

>> No.7141829

>>7138611
i may be on acid right now, but this definition is fucked right? I can only think of them in terms of correspondence now but

>> No.7141842

>>7139470
> smooth
> not differentiable
pick one

>> No.7142487
File: 217 KB, 848x471, wildfedora.png [View same] [iqdb] [saucenao] [google]
7142487

I FUCKING KNEW IT

>> No.7142491

>>7138076

\Gamma function for me

>> No.7142495

>>7138868
Seriously. He's explicitly said that this is very old stuff that today we have decided to ignore for reasons

>> No.7142505

>>7138076
the coolest one to me? sin
the most useful to me? atan

>> No.7142508
File: 247 KB, 1280x720, wildfedora.png [View same] [iqdb] [saucenao] [google]
7142508

Higher quality picture of ugly Asian girl in fedora attending Wildberger lecture.

>> No.7142518

>>7142508
thank you for your hard work

>> No.7142774

>>7138076
Lambert W-Function

>> No.7142786

>>7142774
that's odd, why?
I never considered it good news, if the solution to an equation requires it.

>> No.7142848

Indicator function of the computable reals :^)

>> No.7143150

y f = f (y f)

>> No.7143166
File: 77 KB, 600x600, 1407691122636.jpg [View same] [iqdb] [saucenao] [google]
7143166

y f = (λx.xxx)(λx.xxx)

>> No.7143188

the tautology kind, or the Lorentz transformation, or the string theory equation, or the mass energy equation. But to be funny, the tautology kind.

>> No.7143347
File: 537 KB, 692x577, accept_it.png [View same] [iqdb] [saucenao] [google]
7143347

>>7143188
>the string theory equation
i.e.?

Also
>what's your favorite function?

>> No.7143351

>>7142786
>Lambert W-Function
I just noticed its relevance to the collatz conjecture

>> No.7143362

>>7141296
Nobody said it was smooth, but it is continuous.

>> No.7143377

>>7138076
Thomae's function

>> No.7143396

Wavefunction is god function

>> No.7143400

>>7138076
Gustave's function

>> No.7143402

>>7139716
>NJW is a genius
negro please

>> No.7143407

f(x)=x