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 =2.4221120551369190496071257990979573529884795994716502062707... If I input Maple's output into WolframAlpha (it understands it) EllipticE(I)*sqrt(2)=E(I)*sqrt(2)= 2.30857888069067525459669379819473812065849859340696523283... - 0.522155213609940348327414982109757688196290110066610791396... I EllipticE(sqrt(3)*I)=E(sqrt(3) I) =1.71922354667492421881087059097431773281393098058387700412... - 0.592044437093386507830834807418356168289707419289021527108... I Cheers, Alex On Sep 7, 2:26 pm, William Stein <wst...@gmail.com> wrote: > On Mon, Sep 7, 2009 at 11:12 AM, Alexander > > R.Povolotsky<apovo...@gmail.com> 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 tohttp://sagenb.org/and sign up (which > takes about 10 seconds, no email address required), then you can try > the above out yourself through your web browser. > > Anyway: > > sage: var('t') > t > sage: integrate((cos(t)^6+sin(t)^6)^(1/2), t,0,pi) > integrate(sqrt(sin(t)^6 + cos(t)^6), t, 0, pi) > sage: integrate((cos(t)^4+sin(t)^4)^(1/2), t,0,pi) > integrate(sqrt(sin(t)^4 + cos(t)^4), t, 0, pi) > sage: numerical_integral((cos(t)^4+sin(t)^4)^(1/2), 0,pi)[ 0 ] > 2.701287762095351 > sage: numerical_integral((cos(t)^6+sin(t)^6)^(1/2), 0,pi)[ 0 ] > 2.4221120551366173 > > By the way, I computed the numerical integrals above, to get specific > numbers, in case you're interested.... for some applications that > might help. > > William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
