can the prime really not solve this integral?
02-28-2014, 05:47 AM (This post was last modified: 02-28-2014 05:48 AM by DeucesAx.)
Post: #21
 DeucesAx Junior Member Posts: 20 Joined: Feb 2014
RE: can the prime really not solve this integral?
(02-27-2014 07:08 PM)parisse Wrote:  We almost never test the CAS in degree mode, therefore more bugs are expected there. The reason here is that for numeric integration with an infinite boundary you must make a change of variable, here we set tan(y)=x for y in 0..pi/2, dx=(1+tan(y)^2)*dy ... except that in degree mode you must add a pi/180 factor.

No pressure, I'm sure once I'm done with college the prime will be a formidable calculator. And heck, I just need to eat rahmen noodles instead of regular pasta for the next 6 month to pay for the prime, no biggie.

(02-27-2014 09:11 PM)Manolo Sobrino Wrote:  That integral appears when you integrate the Planck distribution to all frequencies in order to recover the Stefan-Boltzmann law, also in the Debye theory of specific heat. The functions defined by these integrals are called Debye functions. See Abramowitz-Stegun §27.1
Well at least I now know that I did the simplification by hand to get there correctly. Thank the spaghetti monster almighty.
02-28-2014, 07:59 AM
Post: #22
 parisse Senior Member Posts: 1,086 Joined: Dec 2013
RE: can the prime really not solve this integral?
(02-27-2014 09:11 PM)Manolo Sobrino Wrote:
(02-27-2014 12:21 PM)parisse Wrote:  You get a numeric answer with:
int(x^3/(exp(x)-1),x,0,inf)
then shift-enter.
x^3/(exp(x)-1) does not have an antiderivative than you can express with elementary function (special functions required, polylogs here). There is probably a trick than can give you the exact answer (pi^4/15) for the definite integral, any idea? On a voyage 200, you don't get the exact value by the way.

No, no, you don't use primitives for this, come on.
You could use contour integration/Residue Theorem, but it's a bit tricky for this. See for instance:

http://en.wikipedia.org/wiki/Stefan_bolt...w#Appendix

The easy way is:

http://math.stackexchange.com/questions/...u3-eu-1-du
That's exactly what I meant by a trick to find the exact answer for the definite integral.

Quote:(Now that I'm thinking about it, it shouldn't be too difficult to implement a large class of definite integrals by the Residue theorem. That would be come in handy.)
There is already a class of definite integrals that are handled by the residue theorem. But this one requires a trick before one can apply it, I can not implement that. Expanding 1/(exp(x)-1) is a better trick, but I don't know if that can lead to something sufficiently general (I don't like tables). And it's not that important anyway, since the numeric answer is reliable.
02-28-2014, 08:15 AM
Post: #23
 jebem Senior Member Posts: 1,320 Joined: Feb 2014
RE: can the prime really not solve this integral?
(02-28-2014 04:52 AM)rkf Wrote:
(02-27-2014 07:08 PM)parisse Wrote:  We almost never test the CAS in degree mode, therefore more bugs are expected there. The reason here is that for numeric integration with an infinite boundary you must make a change of variable, here we set tan(y)=x for y in 0..pi/2, dx=(1+tan(y)^2)*dy ... except that in degree mode you must add a pi/180 factor.

Interestingly enough, both HP50g, and TI-92 Plus, give a numerically correct approximation to the exact answer (pi^4/15) independent of the degree/radiant setting :-)

Yes, to use a HP-Prime properly, I would recommend to have a HP-50G by hand, just in case.
I tried to solve it on my 4 years old HP-50G, and voilá, the numeric answer was easy to get (pls see attachments).

Jose Mesquita

02-28-2014, 08:50 AM
Post: #24
 parisse Senior Member Posts: 1,086 Joined: Dec 2013
RE: can the prime really not solve this integral?
(02-28-2014 05:47 AM)DeucesAx Wrote:
(02-27-2014 07:08 PM)parisse Wrote:  We almost never test the CAS in degree mode, therefore more bugs are expected there. The reason here is that for numeric integration with an infinite boundary you must make a change of variable, here we set tan(y)=x for y in 0..pi/2, dx=(1+tan(y)^2)*dy ... except that in degree mode you must add a pi/180 factor.

No pressure, I'm sure once I'm done with college the prime will be a formidable calculator. And heck, I just need to eat rahmen noodles instead of regular pasta for the next 6 month to pay for the prime, no biggie.
From your first post in this thread, it seems you already own a ti89 and a ti nspire CAS, therefore I don't believe you will really need 6 months of restrictions to pay your Prime.
FYI, I have already fixed the bug and sent the patch to HP. I make my best to fix bugs as soon as I know them and publish corrected version of Xcas, but I'm obviously not responsible for HP firmware releases. In the meantime, put your calculator in radian, that's the normal unit of angle when using a CAS.
02-28-2014, 11:30 AM
Post: #25
 CR Haeger Member Posts: 275 Joined: Dec 2013
RE: can the prime really not solve this integral?
(02-28-2014 05:47 AM)DeucesAx Wrote:  No pressure, I'm sure once I'm done with college the prime will be a formidable calculator. And heck, I just need to eat rahmen noodles instead of regular pasta for the next 6 month to pay for the prime, no biggie.

Cool - hurry up and graduate
02-28-2014, 11:42 AM (This post was last modified: 02-28-2014 11:47 AM by CR Haeger.)
Post: #26
 CR Haeger Member Posts: 275 Joined: Dec 2013
RE: can the prime really not solve this integral?
(02-28-2014 01:51 AM)jte Wrote:  Are you performing a signed area computation for X^3/(e^X-1), from 0 to 100, in the Function app Plot view? I just tried this on the emulator and on the device. Neither hanged for me — both quickly brought up a numerical approximation.

Can you reliably reproduce the hang?

Yes - both hang at "calculating" for me 0--> any positive number. On Symb to reset. Dont know if related to CAS settings pg 2: 10, 1, 100, 1E-12, 1E15 and 40 in order or something else.

Also noted that in CAS, integrating 0 to say >1500 starts giving "adaptive method failure, will try with Romberg..." error. Integrating 0--> <1500 gives 6.49 approximation.
02-28-2014, 11:19 PM
Post: #27
 jte Member Posts: 69 Joined: Feb 2014
RE: can the prime really not solve this integral?
(02-28-2014 11:42 AM)CR Haeger Wrote:
(02-28-2014 01:51 AM)jte Wrote:  Are you performing a signed area computation for X^3/(e^X-1), from 0 to 100, in the Function app Plot view? I just tried this on the emulator and on the device. Neither hanged for me — both quickly brought up a numerical approximation.

Can you reliably reproduce the hang?

Yes - both hang at "calculating" for me 0--> any positive number. On Symb to reset. Dont know if related to CAS settings pg 2: 10, 1, 100, 1E-12, 1E15 and 40 in order or something else.

Also noted that in CAS, integrating 0 to say >1500 starts giving "adaptive method failure, will try with Romberg..." error. Integrating 0--> <1500 gives 6.49 approximation.

I've just tried it here on a device with the CAS settings above (with 1E-15 for the "Probability" setting), but a numerical approximation simply came up quickly. What firmware are you using? Does it occur with default factory settings on your device? To be sure we're looking at the same function, would it be convenient / possible for you to post a photo of the SYMB view?
03-01-2014, 12:03 AM
Post: #28
 CR Haeger Member Posts: 275 Joined: Dec 2013
RE: can the prime really not solve this integral?
Thanks jte.

Using latest 11/25 ROM on both hhc.

I'll try to send along a SYMB screenshot.
03-01-2014, 05:52 AM
Post: #29
 jte Member Posts: 69 Joined: Feb 2014
RE: can the prime really not solve this integral?
I've just tried rev. 5447 (the Nov 25, 2013 release) on my device here and it didn't hang in the signed area computation in the Function plot view.

I did manage to recreate the "adaptive method failure, will try with Romberg…" in the CAS view.
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