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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

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)*

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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Here's some plot:

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

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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Here's some 3d:

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

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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And here's the imaginery part:

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

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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And my question: why this foundamental function is so complicated?

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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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)*

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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Then the immagineric part is ostilating too.

IPBLE: Increasing Performance By Lowering Expectations.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,651

Very nice plots

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

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)*

**igloo** **myrtilles** **fourmis**

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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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)*

IPBLE: Increasing Performance By Lowering Expectations.

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**John E. Franklin****Member**- Registered: 2005-08-29
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Can you point me to a link to read more about this subject?

I feel kind of dumb looking at this.

**igloo** **myrtilles** **fourmis**

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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You can start here:

Wikipedia

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**John E. Franklin****Member**- Registered: 2005-08-29
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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)?

**igloo** **myrtilles** **fourmis**

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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???

I don't know.

I'll see.

Very interesting argument.

IPBLE: Increasing Performance By Lowering Expectations.

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