Prev: How to get 90 degree phase shift
Next: Removing columns
From: Vladimir Bondarenko on 12 Jul 2010 03:43
Hello,

erfc(3/2*(-1)^(3/4))
+erfc((1-I)*(1+sqrt(2)/4))
+(1+I)*(I*FresnelC(3/sqrt(2*Pi))
-I*FresnelC(2/sqrt(Pi)+1/sqrt(2*Pi))
-FresnelS(3/sqrt(2*Pi))
+FresnelS(2/sqrt(Pi)+1/sqrt(2*Pi))
);

?
Cheers,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester Ltd.

----------------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

----------------------------------------------------------------
----------------------------------------------------------------

http://groups.google.com/group/sci.math/msg/9f429c3ea5649df5

"...... the challenges imply that a solution is built within the
framework of the existent CAS functions & built-in definitions."

----------------------------------------------------------------
----------------------------------------------------------------
From: Mate on 12 Jul 2010 04:37
On Jul 12, 10:43 am, Vladimir Bondarenko <v...(a)cybertester.com> wrote:
> Hello,
>
>  erfc(3/2*(-1)^(3/4))
> +erfc((1-I)*(1+sqrt(2)/4))
> +(1+I)*(I*FresnelC(3/sqrt(2*Pi))
>        -I*FresnelC(2/sqrt(Pi)+1/sqrt(2*Pi))
>        -FresnelS(3/sqrt(2*Pi))
>        +FresnelS(2/sqrt(Pi)+1/sqrt(2*Pi))
>        );
>
>                       ?

evalc(simplify(value(convert(%,compose,erf,Int,exp))));

2


Mate
From: Vladimir Bondarenko on 12 Jul 2010 05:06
On Jul 12, 11:37 am, Mate <mmat...(a)personal.ro> wrote:
> On Jul 12, 10:43 am, Vladimir Bondarenko <v...(a)cybertester.com> wrote:
>
> > Hello,
>
> >  erfc(3/2*(-1)^(3/4))
> > +erfc((1-I)*(1+sqrt(2)/4))
> > +(1+I)*(I*FresnelC(3/sqrt(2*Pi))
> >        -I*FresnelC(2/sqrt(Pi)+1/sqrt(2*Pi))
> >        -FresnelS(3/sqrt(2*Pi))
> >        +FresnelS(2/sqrt(Pi)+1/sqrt(2*Pi))
> >        );
>
> >                       ?
>
> evalc(simplify(value(convert(%,compose,erf,Int,exp))));
>
>                                   2
>
> Mate

Perfect!

I wonder if you'd like to try to crack Mr. Py's challenge? :)

http://groups.google.com/group/sci.math.symbolic/browse_thread/thread/c056c0c768d26b56#

(I do remember your desire for a good motivation about the
challenges; in fact, almost all of them are not the random
ones; even better, once I promised you to disclose publicly
the reason why these challenges are the links of the same
chain; now I am closer to such a position; I hope to reach
it within 12-24 months...)

Best wishes,

Vladimir
From: Mate on 12 Jul 2010 05:50
On Jul 12, 12:06 pm, Vladimir Bondarenko <v...(a)cybertester.com> wrote:
> On Jul 12, 11:37 am, Mate <mmat...(a)personal.ro> wrote:
>
>
>
> > On Jul 12, 10:43 am, Vladimir Bondarenko <v...(a)cybertester.com> wrote:
>
> > > Hello,
>
> > >  erfc(3/2*(-1)^(3/4))
> > > +erfc((1-I)*(1+sqrt(2)/4))
> > > +(1+I)*(I*FresnelC(3/sqrt(2*Pi))
> > >        -I*FresnelC(2/sqrt(Pi)+1/sqrt(2*Pi))
> > >        -FresnelS(3/sqrt(2*Pi))
> > >        +FresnelS(2/sqrt(Pi)+1/sqrt(2*Pi))
> > >        );
>
> > >                       ?
>
> > evalc(simplify(value(convert(%,compose,erf,Int,exp))));
>
> >                                   2
>
> > Mate
>
> Perfect!
>

Hello Vladimir,

actually the answer should have been even shorter (without the erf
converson) but there is
a _severe bug_ in convert/Int for erfc where erfc is treated as
erfi !!!
The wrong (integral) definition appears in FunctionAdvisor for erfc.
I mention this because I know you collect such material.

Mate

From: Axel Vogt on 12 Jul 2010 06:08
Mate wrote:
....
> actually the answer should have been even shorter (without the erf
> converson) but there is
> a _severe bug_ in convert/Int for erfc where erfc is treated as
> erfi !!!
> The wrong (integral) definition appears in FunctionAdvisor for erfc.
> I mention this because I know you collect such material.
>
> Mate
>

Yes, at least for Maple 12 there is a bug.

erfc(x):
% = convert(%, Int);
value(%);

erfc(x) = -I erf(x I)

 |  Next  |  Last
Pages: 1 2
Prev: How to get 90 degree phase shift
Next: Removing columns