Re: Integrate Result depends on symbol used
- To: mathgroup at smc.vnet.net
- Subject: [mg42890] Re: Integrate Result depends on symbol used
- From: adam.smith at hillsdale.edu (Adam Smith)
- Date: Fri, 1 Aug 2003 01:26:00 -0400 (EDT)
- References: <bg7vj2$hi7$1@smc.vnet.net> <bgaaos$se9$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
FYI. The integral evaluates just fine with "x" on my machine:
Mathematica 4.1 running Windows 2000.
Integrate[Sqrt[y - x]/(y^2 Sqrt[1 - y^2]), { y , x, 1},
Assumptions -> {x > 0, x < 1}]
Out[4]=
(1/4)*Pi*(2/Sqrt[x] - (2*Sqrt[2*Pi]*HypergeometricPFQ[{-(1/4), 1/4,
3/4}, {1/2, 5/4},
x^2])/(Gamma[1/4]*Gamma[5/4]) +
(Sqrt[2*Pi]*x*HypergeometricPFQ[{1/4, 3/4, 5/4}, {3/2, 7/4}, x^2])/
(Gamma[-(1/4)]*Gamma[7/4]))
I recall that there was a similar type of observation in the last year
or two. Unfortunately, I don't remember the specifics. However it is
worth being aware of this behavior of some integrals involving the
common variables x, y and z.
Adam Smith
"Bill Bertram" <wkb at ansto.gov.au> wrote in message news:<bgaaos$se9$1 at smc.vnet.net>...
> "Jim Hanson" <hanson at physics.auburn.edu> wrote in message
> news:bg7vj2$hi7$1 at smc.vnet.net...
> > Mathematica's ability to do a definite integral depends on the symbol
> > used.
> > Here's an example with Mathematica 5.0.0.0 on a Macintosh running OSX
> 10.2.6.
> > Note that Mathematica can do the integral with a symbol z
> > (which comes after the variable of integration y in the alphabet) but
> > can't do it with a symbol x. This seems very odd to me. Does anyone
> > know why this happens?
> >
> > In[1]:= Integrate[Sqrt[y - x]/(y^2 Sqrt[1 - y^2]), { y , x, 1},
> > Assumptions -> {x > 0, x < 1}]
> >
>
>
> Same on a PC running Windows XP. Really amazing! If you change "y" to "w"
> (ie one letter before "x") in the above expression, the integral is again
> evaluated.
>
> Cheers,
> Bill