Hi sci! I'm a musician and i need a little help. I need

>>8025000
>f(0) = 0
>f(x) < 0 ∀ x

Uh.

>>8025000
>f(x) < 0 ∀ x
That's not how you use quantifiers (I know what you're trying to say, but that's not proper syntax).

>>8025000
>f(x) < 0 ∀ x
>lim x-> +inf f(x) = 1
What.

Also,
>f(0) = 0
>f(x) < 0 ∀ x
>f'(0) = 1

And >>>/sqt/

>>8025024
>>8025000

I'm so sorry, I meant f(x) < 1 ∀ x
But thinking it again, I just need a horizontal asymptote and f(x) < lim x-> +inf f(x)
I can normalize my result later

Try f(x) = a*arctan(b*x) for some appropriate constants a and b.

>>8025036
That's much easier. How about 1-e^(-(x^2)?
Upside down bell curve! Best function.

>>8025036
tanh(x)

f(x) = x / (abs(x) + c) should do the job for all positive c.

>>8025030
>bitches about syntax
>doesn't provide anything helpful about proper syntax
Kill yourself

So you know, OP, most people put their quantifies in front of their conditional statements and you should probably include a set. So say something more like "for all x in R, f(x)<1" instead of "f(x)<1 all x"

>>8025000
tanh(x) is exactly what you need

>>8025050
>>8025044
>>8025041
>>8025038

This is the result, just a first try...
You can see the waveform of the original sine,atan, tanh, x / (abs(x) and 1-e^(-(x^2).
tanh is nice, but the Upside down bell curve is interesting. =)

Ty m8! XD

File: ws.png (64KB, 1284x644px) Image search: [Google]

64KB, 1284x644px

>>8025184

File: wave.jpg (29KB, 963x132px) Image search: [Google]

29KB, 963x132px

>>8025220
Making sound with help of math and programming?
I have the same hobby :D
Pic related, program I'm writing from scratch.

I'm more a musician than a programmer, I work with max/msp to make audio and video. This sketch is made for try with a simple compressor/waveshaper. The arctan give nice results for it's simplicity!

>>8025000
fourier series

It's not really a class of functions, but it sounds like you're interested in sigmoid functions OP. This is a bunch of functions that are generally S-shaped (like 1/tan x) and they're used a lot in machine learning and statistical stuff in general. There's a good list on wikipedia: https://en.wikipedia.org/wiki/Sigmoid_function

>>8025000
> f(0) = 0
> f(x) < 0 for any x

You mean for any x except x = 0?

>>8025000
Can it be piecewise? Does it need to be continuous and differentiable at x = 0? You could do something like the following:

f(x) = {1 - 1/x, x > 1; 0, -1 < x < 1, 1 + 1/x, x < -1}.

>>8026006

Yep! I really like sigmoid curves!!! Thanks!!!

>>8026059
Whoops. fucked that one up. I meant the following:

f(x) = {1 - 1/x, x > 1; -(x^3) + x, -1 < x < 1, 1 + 1/x, x < -1}.

This way, you have f'(0) = 1, f(0) = 0, and f(x) < 1 for all real values of x. Finally, lim x -> +infinity of f(x) = 1. This is continuous (f(1) = 0 and f(-1) = 0) for all real values of x, but not differentiable for +/- 1.

>>8025233
Just use a synth and its ADSR desu, it's easier.

>>8026006

>>8026006
The erf function looks pretty good, especially because i can use it as a class of functions and change the graph in real time.

My problem is that it's a integral function! I know that i only need to find out a primitive of the integral part and and take the difference between F(0) and F(x), but the point is that I don't know hot to integrate that! I just have a high scool education in math, sorry.

I have tried with https://www.wolframalpha.com/input/?i=integral+e%5E(-x%5E2) but is not useful to me.