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I am posting this for a friend. Please post or e-mail to me.
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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

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