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MathGroup Archive 2007

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Re: AiryAi

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75888] Re: AiryAi
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Sat, 12 May 2007 03:19:22 -0400 (EDT)
  • References: <f1hlg0$p7q$1@smc.vnet.net>

Anton and Maxim thanks a lot for your invaluable information.

Dimitris

=CF/=C7 dimitris =DD=E3=F1=E1=F8=E5:
> Hello.
>
> Consider the integral
>
> In[678]:=
> f = HoldForm[Integrate[AiryAi[o], {o, a, b}]]
>
> Then
>
> In[679]:=
> {ReleaseHold[f /. {a -> 0, b -> Infinity}], (Rationalize[#1, 10^(-12)]
> & )[
>    ReleaseHold[f /. Integrate -> NIntegrate /. {a -> 0, b ->
> Infinity}]]}
>
> Out[679]=
> {1/3, 1/3}
>
> Hence, the symbolic and the numerical result agree.
>
> Next,
>
> In[682]:=
> ReleaseHold[f /. {a -> -Infinity, b -> 0}]
> N@%
>
> Out[682]=
> 2/3
> Out[683]=
> 0.6666666666666666
>
> I think I can trust the last analytic result.
>
> However, no matter what options I set for NIntegrate, I could get a
> satisfactory
> result from its application for the integral in (-infinity,0].
>
> I really appreciate any help.
>
> Thanks
> Dimitris



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