Very interesting function

krassi_holmz · 2006-03-02 22:53:26

Here's some very interesting function:

I'm making plots now.
It's pity that I can't upload 3D .vrml format in the forum.

Last edited by krassi_holmz (2006-03-02 23:03:41)

krassi_holmz · 2006-03-02 23:29:18

Here's some plot:

Last edited by krassi_holmz (2006-03-02 23:31:08)

krassi_holmz · 2006-03-02 23:33:17

Here's some 3d:

Last edited by krassi_holmz (2006-03-02 23:34:39)

krassi_holmz · 2006-03-02 23:36:07

And here's the imaginery part:

Last edited by krassi_holmz (2006-03-02 23:37:25)

krassi_holmz · 2006-03-02 23:38:32

And my question: why this foundamental function is so complicated?

krassi_holmz · 2006-03-02 23:41:04

Here's another: when x and y are negative the real part becomes to ostilate:

Last edited by krassi_holmz (2006-03-02 23:42:18)

krassi_holmz · 2006-03-02 23:43:21

Then the immagineric part is ostilating too.

MathsIsFun · 2006-03-03 00:32:30

Very nice plots

John E. Franklin · 2006-03-03 04:15:14

What does the Capital Gamma letter mean?
Is it a product repeated with integers? If so, why are the plots continuous?

What does the exclamation point mean?
Is it factorial?

Last edited by John E. Franklin (2006-03-03 04:17:30)

krassi_holmz · 2006-03-03 08:20:06

The exclamation point IS factorial

It looks quite strange, but actually it's one of the most inportant functions in the contemorary mathematics. There's an equation that connects it with the factorial:
Г(k+1)=k!
But Г is defined over all complex numbers. So that's the generalization of the factorial over the complex numbers.
But there's another too. It may be complex for some arguments so it's plot is 4d: 1 dimention for x, 1 for y, 1 for u and 1 for v, where
Г(x+iy)=u+iv.
That's why there 2 plots for my function: 1 for the real part of the rezult: Re(Г(xy+1)) and one for the imagineric: Im(Г(xy+1))

Last edited by krassi_holmz (2006-03-03 08:27:52)

John E. Franklin · 2006-03-03 15:30:54

Can you point me to a link to read more about this subject?
I feel kind of dumb looking at this.

krassi_holmz · 2006-03-03 19:31:47

You can start here:
Wikipedia

John E. Franklin · 2006-03-04 06:35:08

What made you interested in plotting x * y, and why wouldn't f(.25,.75) = f(.75,.25) ?
x * y = y * x, so where is your line of symmetry (y=x)?

krassi_holmz · 2006-03-04 21:01:26

???
I don't know.
I'll see.
Very interesting argument.

Math Is Fun Forum

#1 2006-03-02 22:53:26

Very interesting function

#2 2006-03-02 23:29:18

Re: Very interesting function

#3 2006-03-02 23:33:17

Re: Very interesting function

#4 2006-03-02 23:36:07

Re: Very interesting function

#5 2006-03-02 23:38:32

Re: Very interesting function

#6 2006-03-02 23:41:04

Re: Very interesting function

#7 2006-03-02 23:43:21

Re: Very interesting function

#8 2006-03-03 00:32:30

Re: Very interesting function

#9 2006-03-03 04:15:14

Re: Very interesting function

#10 2006-03-03 08:20:06

Re: Very interesting function

#11 2006-03-03 15:30:54

Re: Very interesting function

#12 2006-03-03 19:31:47

Re: Very interesting function

#13 2006-03-04 06:35:08

Re: Very interesting function

#14 2006-03-04 21:01:26

Re: Very interesting function

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