Re: Fourier analysis with additional coefficient for the R-matirx

*To*: mathgroup at smc.vnet.net*Subject*: [mg48507] Re: Fourier analysis with additional coefficient for the R-matirx*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Fri, 4 Jun 2004 04:49:21 -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 -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul