Robert Israel clarified that I was incorrect in feeding Maple's output
into WolframAlpha - I am quoting his reply
-- Forwarded message --
From: Robert Israel
I believe Mathematica's EllipticE[x] is Maple's EllipticE(sqrt(x)).
Maple defines EllipticE(k) = int_0^1 sqrt(1 - k^2 t^2)/
Perhaps - I let it be known to Robert Israel who was kindly doing
Maple part for
me. If he reconfirms it - he will pass it along to Maple people, I
presume.
Thanks for helping,
Alex
On Sep 7, 2:43 pm, William Stein wrote:
> On Mon, Sep 7, 2009 at 11:40 AM, Alexander
>
>
>
> R.Povolotsky wrote:
On Mon, Sep 7, 2009 at 11:40 AM, Alexander
R.Povolotsky wrote:
>
> WolframAlpha gives
>
> 2*EllipticE[1/2]=2*E(1/2)=
> (8*Pi^(3/2))/Gamma(-1/4)^2+Gamma(3/4)^2/sqrt(Pi)
> =2.7012877620953510050403494706774516826990447338487090906465...
>
> 2*EllipticE[3/4]=2*E(3/4) =
> Pi*sum_(k=0)^infinity((3/4)
WolframAlpha gives
2*EllipticE[1/2]=2*E(1/2)=
(8*Pi^(3/2))/Gamma(-1/4)^2+Gamma(3/4)^2/sqrt(Pi)
=2.7012877620953510050403494706774516826990447338487090906465...
2*EllipticE[3/4]=2*E(3/4) =
Pi*sum_(k=0)^infinity((3/4)^k*((-1/2)_k (1/2)_k))/(k!)^2
=2.4221120551369190496071257990979573529884795994
On Mon, Sep 7, 2009 at 11:12 AM, Alexander
R.Povolotsky wrote:
>
> Could you try specific "n" cases (4 and 6)
>
> sage: integrate((cos(t)^n+sin(t)^n)^(1/2), t,0,pi)
>
> and
>
> sage: integrate((cos(t)^6+sin(t)^6)^(1/2), t,0,pi)
>
> Thanks,
> Alex
Sure. By the way, if you go to http://sagenb.org/
Could you try specific "n" cases (4 and 6)
sage: integrate((cos(t)^n+sin(t)^n)^(1/2), t,0,pi)
and
sage: integrate((cos(t)^6+sin(t)^6)^(1/2), t,0,pi)
Thanks,
Alex
On Sep 7, 12:28 pm, William Stein wrote:
> On Mon, Sep 7, 2009 at 9:19 AM, Alexander
>
>
>
> R.Povolotsky wrote:
>
> > For
> > Int
On Mon, Sep 7, 2009 at 9:19 AM, Alexander
R.Povolotsky wrote:
>
> For
> Int((cos(t)^n+sin(t)^n)^(1/2),t = 0 ... Pi)
> that is
> Integrate[Sqrt[Cos[t]^n + Sin[t]^n], {t, 0, Pi}]
>
> 1) n=4
> Maple gives
> EllipticE(I)*sqrt(2)
> vs
> Mathemtica's
> 2*EllipticE[1/2]
>
> and
> 2) n=6
> Maple gives
>
