Re: int(BesselJ(0,sqrt(x))*exp(x),x)= ?

Bruno Donati <bruno.donati@xxxxxxxxxx> wrote:
> David W. Cantrell a écrit :
>
> > Bruno Donati <bruno.donati@xxxxxxxxxx> wrote:
> >
> >>junoexpress a écrit :
> >>
> >>
> >>>Are you missing a parenthesis?
> >>>
> >>>J
> >>>
> >>
> >>yes, sorry
> >>
> >>primitive of BesselJ(0,sqrt(x))*exp(x) = ?
> >
> >
> > FWIW
> > Mathematica claims to have an answer in closed form in terms of a
> > hypergeometric function:
> >
> > x^(3/2)*Gamma[3/4]*HypergeometricPFQ[{3/4},{1,7/4},
> > -x^2/4]/(2*Gamma[7/4])
> >
> > David
> are you sure?

I apologize! I'm now sure that I typed the wrong integrand. Sorry.

With the correct integrand, Mathematica simply returns the indefinite
integral unevaluated.

David

> It seems to be not the same integrals.
> int(BesselJ(0,sqrt(x))*exp(x),x=0..1)=1.479263559
>
> 1/2*x^(3/2)*GAMMA(3/4)*Hypergeom([3/4],[1,
> 7/4],-x^2/4)/GAMMA(7/4)=.5980218420 with x=1
>
> (calculus with maple)
.

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