"using residues"...
02-03-2015, 09:34 PM (This post was last modified: 02-06-2015 10:21 PM by salvomic.)
Post: #1
 salvomic Senior Member Posts: 1,366 Joined: Jan 2015
"using residues"...
hi all,
I input $$\int_0^{\pi}{\sqrt{1-cos(t)^{2}} dt}$$ and I get 0, after this message: "searching int of sqrt(-taylorx2)*abs(-taylorx2+1)/(2*taylorx2^2) where taylorx2 is on the unit circle, using residues...
But the integral should be equal to \int(\sin(t),0,π), then 2...

What am I missing?

Thank you for help!

salvo

EDIT: I used "exact" in CAS...
What the difference for normal and "rigorous" use?, please...

∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C - DM42 WP34s :: Prime Soft. Lib
02-04-2015, 06:57 AM
Post: #2
 parisse Senior Member Posts: 1,050 Joined: Dec 2013
RE: "using residues"...
Inside Xcas int(sqrt(1-cos(t)^2),t,0,pi) returns 2, I'll check on the emulator.
02-04-2015, 07:56 AM
Post: #3
 salvomic Senior Member Posts: 1,366 Joined: Jan 2015
RE: "using residues"...
(02-04-2015 06:57 AM)parisse Wrote:  Inside Xcas int(sqrt(1-cos(t)^2),t,0,pi) returns 2, I'll check on the emulator.

here in Home it give 2, but with "T" (upper case).
In CAS with "exact result" set (and with "t") it give 0, without the setting it give 2. (approx result)...

∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C - DM42 WP34s :: Prime Soft. Lib
02-04-2015, 09:31 AM
Post: #4
 parisse Senior Member Posts: 1,050 Joined: Dec 2013
RE: "using residues"...
Tried with my latest version of the emulator, I get 2 with default CAS settings (hence exact). Perhaps a good consequence of another bug fix since the last release.
02-04-2015, 09:38 AM
Post: #5
 salvomic Senior Member Posts: 1,366 Joined: Jan 2015
RE: "using residues"...
(02-04-2015 09:31 AM)parisse Wrote:  Tried with my latest version of the emulator, I get 2 with default CAS settings (hence exact). Perhaps a good consequence of another bug fix since the last release.

then good!
In 6975 there's still the bug...

Let's hope a new release soon!

∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C - DM42 WP34s :: Prime Soft. Lib
03-29-2016, 03:15 PM
Post: #6
 Euler Junior Member Posts: 4 Joined: Oct 2015
RE: "using residues"...
How do you use the residue function or the RESIDUE function
seems this function is a ghost function for the HP Prime..

complex mode? program only?...little help here...my goodness..

The help menu is not a help for this...

J
03-29-2016, 04:01 PM
Post: #7
 Euler Junior Member Posts: 4 Joined: Oct 2015
RE: "using residues"...
ok, if you use residue or RESIDUE..make sure that the variable is not used by
the home directory..or something like this..or you will get error messages..

I have two primes and found the error by comparing calculations with the residue function...pretty neat that it works..

Also, the residue function works with both residue(func,z=x) and
residue(func,z,x)...Im pretty sure..the help menu as std is limited..

J
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