Maxima has issues with the
real and imaginary parts of asech(x).
(%i1) realpart(asech(x));
(%o1) asech(x)
(%i2) imagpart(asech(x));
(%o2) 0
In fact, asech(x) has both real and
imaginary parts for real x.
Despite these incorrect evaluations, Maxima
gives correct numerical values for the imaginary part
of asech(x) when x is a number:
(%i3) imagpart(asech(1.5));
(%o3) 0.84106867056793
(%i4) imagpart(asech(-1.5));
(%o4) 2.300523983021863
However the incorrect evaluation
imagpart(asech(x)) --> 0
prevents quad_qags from finding the
correct value of a simple numerical integral:
(%i5) quad_qags(imagpart(asech(x)),x,1.1,2);
(%o5) [0.0,0.0,21,0]
(The correct answer is about 0.748336.)
Likewise, Maxima gives correct
numbers for the real part if x
is a number, but quad_qags returns
a noun form for what should be a
simple integral:
(%i6) realpart(asech(1.1));
(%o6) 2.2204460492503128E-16
(%i7) realpart(asech(1.2));
(%o7) 0
(%i8) realpart(asech(0.999));
(%o8) 0.044740005477517
(%i9) quad_qags(realpart(asech(x)),x,0.999,1.2);
(%o9) quad_qags(asech(x),x,0.999,1.2,epsrel = 1.0E-8,epsabs = 0.0,limit =
200)
-----------------------------
On Nov. 22, I demonstrated similar problems with acosh(x).
Ted Woollett
(v. 5.25.1gcl, Windows)