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binomial equation

Defines: 
cyclotomic equation
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

11C08 no label found12E05 no label found

Comments

Jussi,

Do you have a reference for this term? I've never seen it used (at least not for this).

Roger

Dear Roger,

I know that the term "binomial equation" is rare in the English language, at least in America, but since it is quite good term, I wanted to tell it in PM. Unfortenately, I have no algebra books in English. Here some Engl. references in internet:
http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=3536
http://www.answers.com/topic/binomial-equation?cat=technology
http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange

In Europe, the equivalents of the term are more used, e.g. in German "binomische Gleichung", ref.
http://www-user.tu-chemnitz.de/~syha/lehre/baI/baI.pdf

in Swedish "binomisk ekvation", ref.
www.matematik.lu.se/matematiklth/personal/sigrid/analys1/lektion19.ps

Jussi

Harry Hochstadt in his book on special functions uses the same sort
of terminology when referring to Mellin's work on integral
representations and differential equations for certain algebraic
functions such as the general solution of the quintic. (Again
the Finnish connection!) To be sure, there the term used is
"trinomial equation", but that is because the equation considered
there has three terms as opposed to two.

While this might sound unusual to Americans --- here, the term
"binomial" is usually appears in the context of binomial
expansions and binomial coefficients, the usage is quite
logical. Just as the words "monomial" and "polynomial" refer
to algebraic expressions with one or many terms respectively,
so too the terms "binomial", "trinomial" are used to refer to
expressions with two and three terms, respectively and the
terms "binomial equation" and "trinomial equation" refer to
equations gotten by setting such expressions to zero.

By the way, Jussi, could you add the form of Mellin's inversion
formula for his transform to your entry on that topic? I would
like to attach an entry explaining Mellin's ingenious use of
inverting a linear transform to the solve non-linear problem
of inverting a trinomial or other algebraic, even transcendental,
function.

> By the way, Jussi, could you add the form of Mellin's
> inversion formula for his transform to your entry on
> that topic? I would like to attach an entry explaining
> Mellin's ingenious use of inverting a linear transform
> to the solve non-linear problem of inverting a trinomial
> or other algebraic, even transcendental, function.

Raymond,
There is no entry on Mellin's transform and its inversion in PM, but a request on it. I cannot write such an entry since I don't know this subject, but I understand that you know. I would be very happy if you could write on those things. (In the biography of Mellin I have mentioned the transform and its inverse.)
Jussi

One Mellin transform entry coming right up!

> One Mellin transform entry coming right up!

Raymond,
I see you have been very hectic and have not yet had time for writing on the transform. I hope you have not forgot the thing =o)
Jussi

No, I did not forget. As you said, I am busy.
This is one of many items on my list of things
to do, including also, for instance, writing
more about C*-algebras and finishing the treatment
of Riemann surfaces from the standpoint of sheaf theory.

Oh, you have so much works! I have only one (a linguistic one).

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