1. polynomials

Hi,
Does anybody recognize the following sequence of real polynomials?
P₁(x)=x, P_{2n}(x)=(x+1)P_{2n-1}(x)+x, P_{2n+1}(x)=(x+1)P_{2n}(x)

Some many years ago I studied a few properties of this sequence, but I forgot where it comes from.

Regards,
Aurel Sp[ataru

2. Formatting problem or new notation?

Unless you are using a notation completely unknown to me, I cannot tell exactly what you mean from your message below:

P₁(x)=x, P_{2n}(x)=(x+1)P_{2n-1}(x)+x, P_{2n+1}(x)=(x+1)P_{2n}(x)

The "_{...}" in particlular is new to me.

I am used to seeing polynomials using subscript index numbers for coefficients or functions, and superscript for exponents. I have never seen underscore followed by braces and have no idea what it may mean.

Do you mean "P sub 2n times x" or "P sub 2n of x" ?

Bye.

Unless you are using a notation completely unknown to me, I cannot tell exactly what you mean from your message below:

P₁(x)=x, P_{2n}(x)=(x+1)P_{2n-1}(x)+x, P_{2n+1}(x)=(x+1)P_{2n}(x)

The "_{...}" in particlular is new to me.

I am used to seeing polynomials using subscript index numbers for coefficients or functions, and superscript for exponents. I have never seen underscore followed by braces and have no idea what it may mean.

Do you mean "P sub 2n times x" or "P sub 2n of x" ?

Bye.
Sorry i have to disagree with you here, there is very little ambiguity in Aurel Spataru notation had it wrapped it around a latex tag it would have been easier on the eye though. the definition is

$P_{1}(x) = x$
$P_{2n}(x)=(x+1)P_{2n-1}(x)+x$
$P_{2n+1}(x)=(x+1)P_{2n}(x)$

(yes i just wrapped what he wrote in math tags)

Bobak

4. LaTex vs. Polynomials

Thanks, I had guessed that there were subscripts, but I could not be sure.

I hope someone writes an interesting analysis.

A digression:

I do not have LaTex nor do I know what math tags are.

I once attempted to download LaTex but it was such a huge file that I abandoned the attempt. On seeing the arcane coding required to use LaTex I decided it would be a step backwards in text formatting.

The only advantage I can see in LaTex so far is that it is supported by this editor and similar sites.

I use MS Excel to write and print just about any math text I need and can print it to pdf files for those who cannot view MS Excel. For my personal use I need only print it for the intended user.

Excel has a WYSIWYG interface and anyone who can cut-and-paste can use it on their first attempt without further training or memorizing arcane coding. Further, Excel has the advantage of calculation. The only down side is that it is not supported by this editor.

I know that the LaTex users of this world will not be convinced that there are other options, particlarly because each one of them has (1) invested a lot of time memorizing the arcane coding rquired to use LaTex, and (2) is reinforced by communicating with like-minded individuals.

Consequently I will not digress further.

I do not have LaTex nor do I know what math tags are.

Exactly try and find out before making such uninformed and inaccurate comments.

Bobak

6. Originally Posted by Aurel Spataru
Hi,
Does anybody recognize the following sequence of real polynomials?
P₁(x)=x, P_{2n}(x)=(x+1)P_{2n-1}(x)+x, P_{2n+1}(x)=(x+1)P_{2n}(x)

Some many years ago I studied a few properties of this sequence, but I forgot where it comes from.
The formula for P_{2n}(x) is $P_{2n}(x) = \frac{(x+1)^{2n-1}(x^2+3x+1) - 1}{x+2}$, as you can easily prove by induction. But I don't recognise this sequence from any other context.

7. are you THE Aurel Spataru?