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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Supposing you want the gf of the Fibonacci numbers and do not know the recurrence.

You start with the Taylor series expansion, the bread and butter of numerical analysis.

The fibonacci numbers 1, 1, 2, 3, 5, 8, 13...

you say

First term to fit is just

next term is

the next is

You can form a 3 x 3 simultaneous set if you take the first 3 values of the sequence as the RHS.

a = 1 , b = -1 , c = - 1

and the gf is

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Hi bobbym,

Would you kindly give me a introduction to gfs? What do I have to know to start learning about them?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Here is a short intro : topics in gf, you only need to know what polynomials are!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi Agnishom;

What do I have to know to start learning about them?

As Yoda would say, "That which you need, you already know!"

As gAr said you only need to know what a polynomial is and how to multiply them. It is very helpful if you have access to a CAS or else the multiplications are very tedious. Sort of like 187265341324 x 28715526734. You could do that with pencil and paper but a calculator makes the job much easier, same thing with gf's.

I remember on A's forum you asking about partitions. I answered the question over there for you. Partition problems are done using generating functions.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Hi gAr, Thanks I shall visit the link

Hi bobbym, Yes, I remember that you mentioned them but still I am not yet introduced to it. How are you now?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi Agnishom;

Not so good, I am feeling very drained.

When you are ready with a problem just post it and we will begin doing gf's together.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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