subexpressions (OT: math)

[Wildemar Wildenburger]

Peter Otten wrote:
> Stebanoid at gmail.com wrote:
>
>   
>> sine is a dimensionless value.
>> if we expand sine in taylor series sin(x) = x - (x^3)/6 + (x^5)/120
>> etc.
>> you can see that sin can be dimensionless only if x is dimensionless
>> too.
>>     
>
> With y = x^2 = 1/3 pi^2 - 4(cos x - cos(2x)/2^2 + cos(3x)/3^2 - ...)
>
> area is dimensionless, too, I suppose.
>  
No, its not dimensionless (phew, that took me a while ... got pretty 
anxious there for a moment):

If you look at the definition of the fourier coefficients on the page 
you presented (http://www.exampleproblems.com/wiki/index.php/FS6), 
you'll see that they have
the same unit as f(x) (or y(x) as in your example).
Which, btw,  is VERY MUCH desired because all science (and with it the 
universe, mind you!) would blow up if functions didn't  have the same 
unit as any of their series expansions. After all, they are meant to 
*replace* the function.
Man! You scared me good!
:D


Oh my, remember when we used to discuss murderous snakes and silly 
British comedians on this group?
I hardly do ...
/W