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

Login

Username

Password

Not registered yet?

#1 2013-01-19 16:37:17

bobbym
Administrator

Offline

Getting the generating function.

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#2 2013-01-19 23:53:33

Agnishom
Real Member
Award: Wink Sherlock

Offline

Re: Getting the generating function.

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


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda

#3 2013-01-20 01:47:08

gAr
Star Member

Online

Re: Getting the generating function.

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."

#4 2013-01-20 12:21:16

bobbym
Administrator

Offline

Re: Getting the generating function.

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2013-01-20 23:36:34

Agnishom
Real Member
Award: Wink Sherlock

Offline

Re: Getting the generating function.

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?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda

#6 2013-01-20 23:51:35

bobbym
Administrator

Offline

Re: Getting the generating function.

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Board footer

Powered by FluxBB