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From: joel on 17 Jul 2010 12:37
I found a way to express this (2^x-1)^j differently... kinda like an identity.
I want to know every identity with this expression so I can see if mine already exists.
Anyone knows a book with every possible identity?
or possibly a link (i've tried to find a website but i couldnt) thanks you
From: Tim Little on 17 Jul 2010 22:21
On 2010-07-17, joel <kenny_914(a)hotmail.com> wrote:
> I found a way to express this (2^x-1)^j differently... kinda like an
> identity. I want to know every identity with this expression so I
> can see if mine already exists. Anyone knows a book with every
> possible identity?

There are no such books, as there are extraordinarily many identities
that have been published throughout history, many of them being
particular forms of well-known patterns applied to novel situations,
many others very specific to a given expression and not much use
otherwise, and far fewer (though still many) that are generally
useful. Some of the generally useful ones may be collected in some
book somewhere.

If you provide the expression, perhaps someone might happen to recall
or easily find a publication that contains it.


- Tim
From: Ludovicus on 19 Jul 2010 08:59

> I found a way to express this (2^x-1)^j differently... kinda like an identity.
> I want to know every identity with this expression so I can see if mine already exists.

If a formula can be expressed differently then IT IS an identity.
If it is an identity then it already exists.
Ludovicus
From: Chip Eastham on 19 Jul 2010 09:54
On Jul 17, 10:21 pm, Tim Little <t...(a)little-possums.net> wrote:
> On 2010-07-17, joel <kenny_...(a)hotmail.com> wrote:
>
> > I found a way to express this (2^x-1)^j differently... kinda like an
> > identity.  I want to know every identity with this expression so I
> > can see if mine already exists.  Anyone knows a book with every
> > possible identity?
>
> There are no such books, as there are extraordinarily many identities
> that have been published throughout history, many of them being
> particular forms of well-known patterns applied to novel situations,
> many others very specific to a given expression and not much use
> otherwise, and far fewer (though still many) that are generally
> useful.  Some of the generally useful ones may be collected in some
> book somewhere.
>
> If you provide the expression, perhaps someone might happen to recall
> or easily find a publication that contains it.
>
> - Tim

Without knowing more I'd suspect an application
of the binomial theorem or related expansions
are a place to start a literature search.

regards, chip
From: joel on 22 Jul 2010 18:36
Well by the way, I was mistaken in that expression...
it is actualy (2^x+1)^j
And yes it is related to the binomial theorem and represented in a sum of powers of course... I've read that with pascal's triangle arises many many... many many ... and many identities. So the one I got probably exists already, but I won't show it until I see it in a book so that's why I'm wandering if some university teacher would have the generosity of pointing me to a book that goes directly to binomial expansions relating to binary powers...
Mine is already known probably. I still want to see it in a book first.

but this also goes further, there is also (2^n + 2^(n-1) + 1)^j
and so forth.... (2^n + 2^(n-1) + 2^(n-2) .... + 2^1 + 1)^j, which is equal to (2^(n+1)-1)^j which kind comes back to the equation (mersenne number too) in my first post. I will probably figure it binomial form (if that's how you say that) with the right amount of trials and errors. It's a hobby of mine using mathematica... Really nice math program!

anyways thx for the feedback, really appreciated because I have no one to share this with as of now. Really appreciated
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