The (misspelled) functions spherodialwave_a and spherodialwave_b are
supposed to be solutions to A&S 20.1.8. The DEs 20.1.8 and 21.6.4 are
related through a point transformation, I think.
What is the best source for the spheroidal wave functions?
I'll see what I can do about correcting the spelling of these
functions, standardizing to a definitive source, and writing user
documentation.
Sorry for the confusion. Thanks for pointing out these problems.
Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>To:?"'Maxima?List'"?<maxima at math.utexas.edu>
>From:?Leo?Butler?<l.butler at ed.ac.uk>
>Sent?by:?maxima-bounces at math.utexas.edu
>Date:?10/29/2009?04:44AM
>Subject:?[Maxima]?spherodialwave?[sic]
>
>I?recently?found?the?above?named?function?in?a?solution?to?a?2nd-order
>ode.?I?cannot?find?a?definition?of?these?functions,?which?I?suspect
>should?be?called?'spheroidalwave'?functions.?When?I?check?if?they?are
>the?spheroidal?wave?functions?from?A&S?21.6.3&4,?I?find?that?they?are
>not.
>
>What's?going?on?here??Leo
>
>
>(%i73)?des?:?diff(?(-t^2+1)*diff(w,t),?t?)+(l-'c^2*t^2-m^2/(-t^2+1))*w;
>
>(%o73)?(1-t^2)*'diff(w,t,2)-2*t*'diff(w,t,1)+(-m^2/(1-t^2)-c^2*t^2+l)*w
>(%i74)?odelin(des,w,t);
>
>(%o74)
>{spherodialwave_a(-m,-m^2+m+l,c^2/4,-t)/((t-1)^(m/2)*(t+1)^(m/2)),
>?????????spherodialwave_b(-m,-m^2+m+l,c^2/4,-t)/((t-1)^(m/2)*(t+1)^(m/2))}
>(%i75)?des?:?diff(?(t^2+1)*diff(w,t),?t?)-(l-'c^2*t^2+m^2/(t^2+1))*w;
>
>(%o75)?(t^2+1)*'diff(w,t,2)+2*t*'diff(w,t,1)-(m^2/(t^2+1)-c^2*t^2+l)*w
>(%i76)?odelin(des,w,t);
>
>(%o76)?{spherodialwave_a(%i*m,m^2-%i*m+l,-c^2/4,-%i*t)*(t^2+1)^(%i*m/2),
>?????????spherodialwave_b(%i*m,m^2-%i*m+l,-c^2/4,-%i*t)*(t^2+1)^(%i*m/2)}
>
>
>--
>The?University?of?Edinburgh?is?a?charitable?body,?registered?in
>Scotland,?with?registration?number?SC005336.
>
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