On Fri, Oct 20, 2023 at 07:41:31PM -0700, 'Nasser M. Abbasi' via FriCAS - computer algebra system wrote: > Fyi, Rubi and Mathematica 13.3.1 gives answer in terms of Hypergeometric > special function. Not sure if you consider this one the "usual" special > functions you refer to
Currently FriCAS do not use hypergeometric functions in aswers to integration problems. That will probably change in the future, but to justify the answer one needs a lot of hypergeometric function identities and those are scattered in the literature. Worse, while in many places one can find various identities, justifications of the identities seem to be scarce. Also, without ability to simplify hypergeometric answers are of little use, so we need first strong simplifier for hypergeometric functions. In particular we need ability to discover when hypergeometric function (or its derivative) is just a disguise and we are really dealing with something simpler like elementary or Liouvillian function (actually, theory says that all hypergeometric functions useful for integration are disguise, "true" hypergeometric functions can not appear as integrals of simpler functions). > integrand=Cos[t]^(1/3)*(2+Cos[t])/100 > Integrate[integrand,t] > > -(1/1400)3 Cos[t]^(4/3) Csc[t] (7 Hypergeometric2F1[1/2,2/3,5/3,Cos[t]^2]+2 > Cos[t] Hypergeometric2F1[1/2,7/6,13/6,Cos[t]^2]) Sqrt[Sin[t]^2] > > And Rubi gives > > Int[integrand,t] > -((3 Cos[t]^(4/3) Hypergeometric2F1[1/2,2/3,5/3,Cos[t]^2] Sin[t])/(200 > Sqrt[Sin[t]^2]))-(3 Cos[t]^(7/3) Hypergeometric2F1[1/2,7/6,13/6,Cos[t]^2] > Sin[t])/(700 Sqrt[Sin[t]^2]) > > Tried Maxima, Giac and Maple and these all can't solve this either. > --Nasser > > > On Friday, October 20, 2023 at 6:41:52 PM UTC-5 Waldek Hebisch wrote: > > > On Fri, Oct 20, 2023 at 02:21:21PM -0700, Mild Shock wrote: > > > Possible to make FriCAS solve this integral? > > > > > > /* Version: FriCAS 1.3.7, WSL2 */ > > > /* ^(1/3) is supposed to be the real root */ > > > > > > (2) -> integrate(cos(t)^(1/3)*(2+cos(t))/100, t) > > > > > > t 3+-------+ > > > ++ (cos(%A) + 2)\|cos(%A) > > > (2) | ----------------------- d%A > > > ++ 100 > > > > > > > Well, FriCAS claims tha answer is not elementary. Currently > > FriCAS can not find answer in terms of "usual" special > > functions and I do not know if there such an answer. > > > > Note that what is produced above can be treated as ad-hoc > > special function, so there is answer, the question is > > if this is more explicit or simpler answer. > > > > It is not clear what you mean by "Make it work"? If you > > know better answer you could use rewrite rule to change > > FriCAS result to a different one, but this is very limited in > > scope. Due to the way FriCAS integrator works there is no > > way to provide hints. > > > > If this integral is doable in terms of popular special functions, > > there is good chance that it will be handled in the future. > > But not in current version. > > > > -- > > Waldek Hebisch > > > > -- > You received this message because you are subscribed to the Google Groups > "FriCAS - computer algebra system" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/fricas-devel/2ebb3f63-d2e4-42b7-b3a5-9c1c6094777en%40googlegroups.com. -- Waldek Hebisch -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/ZTOro9DVKUH3b7x5%40fricas.org.
