Special delimited oscillators that maxima can't solve it.

On Tuesday 15 April 2008 03:16, J.C. Pizarro wrote:

>>> 1. sin(1/x) ? ? ? ? [0+,2/pi]
>>> 2. cos(1/x) ? ? ? ? [0+,2/pi]
>>>
>>> 3. sin(1/x^2) ? ? ? [0+,sqrt(2/pi)]
>>> 4. cos(1/x^2) ? ? ? [0+,sqrt(2/pi)]
>>>
>>> ...
>>
>> Well, at least sine, cosine, and Fresnel integrals are not hard to
>> compute, and implement in Maxima too.
>
> I don't believe that these integrals are not hard to compute and implement
> because they are new and were unknown for people until now.
>
> Soon, you will get stuck in somewhere of the implementation in ?Maxima
> because this new theory is a rare case that difficult you.
>
> The Fresnel integrals are not related to here, in this harder solving.

Actually, they are related to indefinite integrals:

\int sin(1/x) dx = x sin(1/x) - Ci(1/x),
\int cos(1/x) dx = x cos(1/x) + Si(1/x),
\int sin(1/x^2) dx = x sin(1/x^2) - sqrt(2 pi) C (sqrt(2/pi)/x),
\int cos(1/x^2) dx = x cos(1/x^2) + sqrt(2 pi) S (sqrt(2/pi)/x).

-- 
Alexey Beshenov <al at beshenov.ru>
http://beshenov.ru/
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