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addition formula

Defines: 
addition formulae, subtraction formula, subtraction formulae
Keywords: 
algebraic addition formula
Synonym: 
addition theorem
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

30D05 no label found30A99 no label found26A99 no label found

Comments

May be I missed something, but what is relation of this entry to the entry "persistence of analytic relations"?

The attachment isn't so good.

Well, the new attachment is also not that good to my opinion. I wouldn't attach it to anything.

OK, if you are thought the thing thoroughly, so I can remove the attachement. I have not found any natural attachement. BTW, if you know some good additional exemples, please tell me!

Jussi

Some other good examples would be the addition formulae for elliptic functions. In fact, Weierstrass showed that the only complex analytic functions which have an addition theorem are algebraic functions elliptic functions (or limiting cases such as trigonometric functions).

> In fact, Weierstrass showed that
> the only complex analytic functions
> which have an addition theorem are
> algebraic functions, elliptic functions, or limiting cases
> (such as trigonometric functions).

So, then this is the point! I didn't know this theorem, but now it is clear, that this entry is naturally attached to this theorem. I guess, such theorem is not presented yet in encyclopedia, so I think it would be reasonable if not to make an entry for this theorem, then at least to mention it here (in the entry "addition formula").

Why is there a reference to homogeneous functions
in entry one:
L(x+y)=L(x)+L(y)

Doen't that addition formula hold for any linear function?

Matte

The "linear function" means often such that the values are determined by a first degree polynomial (cf. e.g. http://en.wikipedia.org/wiki/Linear_function) when it is question of real functions. Therefore it is more certain to say "homogeneous linear".

This is in accordance with the entry "homogeneous function" --
such functions in general have a certain degree (the entry speaks of homogeneous functions of degree...); I wanted to speak of homog. function of degree 1, i.e. linear.
So I said "homogeneous linear function" in the entry "addition formula".

Hi

Sometimes yes. However, I think that its use is
more common in areas like mathematical modelling
(a linear model, linear approximation, etc.)

The proper mathematical name for a mapping of the form
L(v)+v is an _affine transformation_. I
added an entry on this.

http://planetmath.org/?op=getobj&from=objects&name=AffineTransformation

On PM a _linear transformation_ is defined here:

http://planetmath.org/?op=getobj&from=objects&name=LinearTransformation

Thus, as a correction for this entry, "linear" should link
to some entry. Also, if it links to the above definition of
linear transformation, there is no need for reference to
the homogeneous entry.

Matte

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