🚀 go-pugleaf

In article <6006@geocub.UUCP> cohen@alioth.greco-prog.fr (Henri Cohen) writes:
>I am posting this for a friend. Please post or e-mail to me.
>-------------------------------------------------------------
>
>We are working on radial spheroidal wave functions of the first
>kind R_mn^1(c,x) (using Flammer's notation). It is currently
>indicated in handbooks that in the limit of large cx:
>  
>     R_mn^1 ---> cos(cx-(n+1)pi/2)
>
>Actually, for our own purposes, we need a more complete expression
>for this behavior (namely including some kind of dependence on m)
>when, whatever x (real or complex from 0 to infinity) c tends to
>infinity.
>
>Moreover, direct numerical computations seem to indicate that for
>cx purely imaginary
>
>     R_mn^1(c,x) < R_mn'^1(c,x) if n>n'.
>
>Has this conjecture been proved?
>Any pointers to the literature and or answers are welcome. Thanks
>in advance.
>
>	J. Curely and R. Georges, Talence France
>
>--------------------------------------------------------------

Some of us experts have never heard of "Flammer" notation. In particular,
what is m for which you need the dependence? 
Usually m would be a parameter for a spherical angular harmonic 
in the range -n <= m  <= n. From what you 
have stated, and the usual results of spherical Bessel functions, it
is utterly trivial to derive the large x radial dependence for complex c. 
It would
be interesting to have a little more background on the modification of 
the spherical equation or the physical situation it describes or the
numerical work you have put into the problem apropos 
sci.math.num-analysis.

I feel I am missing the point or perhaps once again doing someone's 
homework set. Is c taken to be large and x varied,or both together? 
Since c is the separation constant, it may matter.

In short, more details please. :-)

					Mark R. Carter, Ph.D.