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

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Very interesting function

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)


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

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Very interesting function

Here's some plot:

View Image: G(xy+1).GIF

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


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

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Very interesting function

Here's some 3d:

View Image: ReG3d.GIF

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


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

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Very interesting function

And here's the imaginery part:

View Image: ImG3d.GIF

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


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

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Very interesting function

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


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

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Very interesting function

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

View Image: ReG3d-3..0_-3..0.GIF

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


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

krassi_holmz
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Re: Very interesting function

Then the immagineric part is ostilating too.


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

MathsIsFun
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Registered: 2005-01-21
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Re: Very interesting function

Very nice plots


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

John E. Franklin
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Registered: 2005-08-29
Posts: 3,562

Re: Very interesting function

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)


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

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Very interesting function

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)


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

John E. Franklin
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Registered: 2005-08-29
Posts: 3,562

Re: Very interesting function

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


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

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Very interesting function

You can start here:
Wikipedia


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

John E. Franklin
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Registered: 2005-08-29
Posts: 3,562

Re: Very interesting function

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)?


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

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Very interesting function

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


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