MaplePrimes - answers and comments on Question, Fourier coefficient

No subject

pantole — Mon, 14 May 2007 17:28:05 Z

>f:=s->s^s*(1-s)^(1-s)*sin(Pi*s)/Pi; >evalf(int(f(s),s=0..1)); pantole

symbolic bug?

Tim Van Dusen — Mon, 14 May 2007 18:14:06 Z

Or symbolically - and I'm not sure why the multiplication sign (after the s^s) is required for it to evaluate correctly. If you didn't already already have that, along with the missing "evalf" and was wondering why adding the "evalf" or just using the drop-down menu with "approximate" didn't produce the correct result - it has something to do with needing that multiplication sign. This may be a bug. I also noticed that even if I use the "Maple Math" to insert the symbolic here, the multiplication sign is removed. I inserted an image (I just recently figured out how to do that) into my message to show it as intended.

why is it exp(1)/24 ?

Axel Vogt — Mon, 14 May 2007 23:01:24 Z

why is it exp(1)/24 ?

Fourier coefficient

SandorSzabo — Tue, 15 May 2007 10:28:03 Z

See http://www.emis.de/journals/AASF/Vol27/alzer.html Lemma 2. I could prove Lemma 3 by Maple. Sandor

i had a look

Axel Vogt — Tue, 15 May 2007 17:16:01 Z

I had a look at the link. The proof is a bit tricky and uses Lemma 1 (and l'Hospital), yes? I doubt that Maple would do that (it certainly uses algorithms to solve integrals). If you want to mimic the proof it should be possible, but my guess is, that's not what you have in mind. Yesterday I played a bit with the task (symmetry around 1/2 and shifting to 0), but found no answer. What always works: use the command "identify", it converts a numerical answer to a symbolic one if possible (but usually that not a proof, it however mostly lets you guess what you have to show).

Fourier coefficient

SandorSzabo — Mon, 21 May 2007 17:35:13 Z

I agree with you. I haven't known the command "identify", so I tried it in this case and Maple was able to guess e/24 ! Thanks.