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)}
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