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## #1 2016-06-21 17:24:35

jacks
Member
Registered: 2012-11-21
Posts: 132

### functional equation.

If

and
and
Then

Where

please explain me how can i calculate function

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## #2 2016-06-21 17:26:11

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

### Re: functional equation.

You wish to solve the recurrence? And what is W?

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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## #3 2016-06-21 17:27:48

jacks
Member
Registered: 2012-11-21
Posts: 132

### Re: functional equation.

Bobbym actually it is set of whole number

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## #4 2016-06-21 17:35:37

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

### Re: functional equation.

Do you wish to solve the recurrence?

There are a couple of ways to solve that type of recurrence. One uses the auxiliary polynomial.

I am getting

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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## #5 2016-06-22 01:21:07

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

### Re: functional equation.

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

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## #6 2016-06-22 03:53:39

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

### Re: functional equation.

Write the characteristic polynomial of the recurrence. This is found by replacing each

in the recurrence by x^n and dividing by x^(n-k) leaving a monic polynomial of degree k and a nonzero constant term.

Now solve

which you should be able to do.

Understand that this is a book problem used to illustrate a very very simple method. In the real world solving this polynomial is much more challenging and can be done by the methods in the other thread.

There are other methods like using generating functions, which I do not like or use. There are cute EM methods that really shine if you have the computational saavy to use them.

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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## #7 2016-06-23 12:22:49

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

### Re: functional equation.

What is a characteristic polynomial?

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

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## #8 2016-06-23 12:28:05

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

### Re: functional equation.

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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## #9 2016-06-23 13:29:29

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

### Re: functional equation.

That's interesting.

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

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## #10 2016-06-23 13:33:58

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

### Re: functional equation.

Works well on book problems.

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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## #11 2016-06-23 13:36:54

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

### Re: functional equation.

What is the inspiration behind the characterisitc polynomial?

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

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## #12 2016-06-23 13:38:31

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

### Re: functional equation.

That I can not say. It looks like just substitution. You can probably read up on it on the net.

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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## #13 2016-06-23 16:07:39

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

### Re: functional equation.

bobbym wrote:

Works well on book problems.

What are book problems?

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

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## #14 2016-06-23 16:11:14

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

### Re: functional equation.

Hohohohooohooooooahahhahhha! That is a good one.

Book problem: Definition:

Pertaining to math, it is a problem found in a math book.

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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## #15 2016-06-23 17:50:26

Member
Registered: 2016-04-16
Posts: 1,086

### Re: functional equation.

You mean "book" used as a noun and not as a verb.

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #16 2016-06-23 18:47:38

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

### Re: functional equation.

I have never been very good with grammar. Being a bumpkin means talking and writing kind of funny.

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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## #17 2016-06-23 20:12:46

Member
Registered: 2016-04-16
Posts: 1,086

### Re: functional equation.

It does not go into my thick head.

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #18 2016-06-24 04:41:01

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

### Re: functional equation.

When I first came here I had a very hard head too. But they taught me how to sharpen it.

Now I have a sharp hard head.

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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## #19 2016-06-24 04:53:38

Member
Registered: 2016-04-16
Posts: 1,086

### Re: functional equation.

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #20 2016-06-24 13:13:39

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

### Re: functional equation.

Yes, I really could see no use for such a head until the guys over here started a thread about typing with other than their fingers. I of course used my sharpened head and it was easy. It was then that I knew why I had been born...

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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## #21 2016-07-09 22:08:10

jacks
Member
Registered: 2012-11-21
Posts: 132

Thanks bobbym

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## #22 2016-07-10 00:12:41

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

### Re: functional equation.

For the sharpened head stuff or the recurrence?

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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