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#1 2010-11-13 01:41:55

123ronnie321
Member
Registered: 2010-09-28
Posts: 128

Challenge

All u hv to do is find functions satisfying -

f` = g
g`= h
h`= f

f,g,h are different functions.
where f means f(x) and f` means f`(x)


-------
A simpler version -

f` = g
g`= f

f(0) = 1
g(0) = 0
find f(1)

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#2 2010-11-13 11:04:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,476

Re: Challenge

Hi 123ronnie321;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2010-11-15 03:17:57

123ronnie321
Member
Registered: 2010-09-28
Posts: 128

Re: Challenge

i did it this way



Last edited by 123ronnie321 (2010-11-21 04:01:15)

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#4 2010-11-15 05:56:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,476

Re: Challenge

That does not give you the analytical answer. Do you know what those series represent?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2010-11-16 19:25:56

123ronnie321
Member
Registered: 2010-09-28
Posts: 128

Re: Challenge

hi bobby

i tried condensing those series and i got the result very similar to what you posted. I must have made some silly error while calculating.
i wrote the series of e^x, e^wx & e^(w^2)x {where w = complex cube root of unity} and added the three......

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#6 2010-11-17 01:09:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,476

Re: Challenge

Hi;

What you probably did wrong was you forgot to divide by 3.

Where 1,w1 and w2 are the roots of unity.

Same answer as I got. But that is not how I did it.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#7 2010-11-19 17:40:15

sameer mishra
Member
Registered: 2010-08-27
Posts: 64

Re: Challenge

hello friend in my openion you are wrong in frist question

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#8 2010-11-19 17:57:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,476

Re: Challenge

Hi sameer mishra;

sameer mishra wrote:

hello friend in my openion you are wrong in frist question

Comments like that are kind of confusing. Can you be more specific. We both have names which will help to differentiate us from each other.
Do you mean me or 123ronnie321. Please use the usernames.

Sorry, opinions have little weight in mathematics. Just saying someone is wrong is adversarial and unproductive.
You must back up your claims. Can you prove your statement?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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