Perhaps I am not invoking elliptic_e
correctly, but it appears that the definition
given in the help manual does not agree
with interactive use of elliptic_e.
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Maxima 5.25.1 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
(%i1) load(nint);
(%o1) "c:/work2/nint.mac"
(%i2) e (phi,mm) := nint (sqrt (1-mm*sin(x)^2),x,0,phi)$
(%i3) e(2,0.1);
(%o3) 1.9392708750601
(%i4) float(elliptic_e(2,0.1));
(%o4) 1.122244398735427
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Also, I tried Wolfram alpha, which gives
N[EllipticE[2, 0.1]] ------->
1.939270875060100..
Ted Woollett