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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bobbym
2013-01-20 23:51:35

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.

Agnishom
2013-01-20 23:36:34

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?

bobbym
2013-01-20 12:21:16

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.

gAr
2013-01-20 01:47:08

Hi,

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

Agnishom
2013-01-19 23:53:33

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

bobbym
2013-01-19 16:37:17

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

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