Re: Fourier analysis with additional coefficient for the R-matirx
- To: mathgroup at smc.vnet.net
- Subject: [mg48533] Re: Fourier analysis with additional coefficient for the R-matirx
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Fri, 4 Jun 2004 04:50:13 -0400 (EDT)
- Organization: The University of Western Australia
- References: <c9k3l0$fdm$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <c9k3l0$fdm$1 at smc.vnet.net>, "Mars" <MarsJO at pentech.ac.za>
wrote:
> I have simplified the R-matrix theory for calculating cross sections.
> In the equation y, Ci (i=0..2) and u are functions of x and can all be
> calculated.
> The equation is
>
> y(x)=C0(x)+Sum(Bl*C1(x)Pl)+Sum(Tl*C2(x)Pl*cos(u(x)))+Sum(Rl(-C2(x)Pl*sin(u(x)))
This expression is ambiguous:
[1] Do C1(x) and C2(x) depend on l (if not, bring outside the summation)?
[2] Does u(x) depend on l (if not, bring outside the summation)?
> The summation is from l=0..infinity and Pl is the (cosine of the)
> Legendre polynomial.
[3] You mean that the argument of Pl is the cosine of an angle? Is the
angle the same for the transmitted and reflected partial waves? If so,
then y is not just a function of x.
> This is a Fourier series analysis, with the exclusion of the second
> term, and can easily be solved
> for Tl and Rl with mathematica.
> However, I would like to know how one can solve all three Bl, Tl and
> Rl.
Why not write your expression _explicitly_ (in Mathematica notation is a
good choice), indicating all functional and parameter dependencies? For
example,
Sum[b[l] C[1][l][x] LegendreP[l, Cos[Theta[1]]],{l,0,Infinity}]
is quite clear. Otherwise it is difficult or impossible to answer the
question you pose.
Cheers,
Paul
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