#2313 real and imaginary parts asech(x)

None
pending
nobody
None
5
2015-05-09
2011-11-25
No

Despite asech(x) having both real and
imaginary parts,

(%i1) realpart(asech(x));

(%o1) asech(x)

(%i2) imagpart(asech(x));

(%o2) 0

Discussion

  • Ted Woollett

    Ted Woollett - 2011-12-03

    system info:
    Maxima version: 5.25.1
    Maxima build date: 10:2 9/6/2011
    Host type: i686-pc-mingw32
    Lisp implementation type: GNU Common Lisp (GCL)
    Lisp implementation version: GCL 2.6.8

     
  • Kris Katterjohn

    Kris Katterjohn - 2015-05-09
    • status: open --> pending
    • Group: --> None
     
  • Kris Katterjohn

    Kris Katterjohn - 2015-05-09

    I'm getting the following results now (SBCL 1.2.4 + git HEAD). It looks like these are correct, just glancing at some plots.

    Anyone want to confirm? I'm marking this ticket as pending for now.

    (%i1) realpart(asech(x));
    (%o1) log((1/x-sin(atan2(0,1/x-1)/2)*sin(atan2(0,1/x+1)/2)*sqrt(abs(1/x-1))
                                        *sqrt(abs(1/x+1))
                  +cos(atan2(0,1/x-1)/2)*cos(atan2(0,1/x+1)/2)*sqrt(abs(1/x-1))
                                        *sqrt(abs(1/x+1)))
               ^2
               +(cos(atan2(0,1/x-1)/2)*sin(atan2(0,1/x+1)/2)
                +sin(atan2(0,1/x-1)/2)*cos(atan2(0,1/x+1)/2))
                ^2
                *abs(1/x-1)*abs(1/x+1))
     /2
    (%i2) imagpart(asech(x));
    (%o2) atan2((cos(atan2(0,1/x-1)/2)*sin(atan2(0,1/x+1)/2)
                 +sin(atan2(0,1/x-1)/2)*cos(atan2(0,1/x+1)/2))
                 *sqrt(abs(1/x-1))*sqrt(abs(1/x+1)),
                1/x+(cos(atan2(0,1/x-1)/2)*cos(atan2(0,1/x+1)/2)
                    -sin(atan2(0,1/x-1)/2)*sin(atan2(0,1/x+1)/2))
                    *sqrt(abs(1/x-1))*sqrt(abs(1/x+1)))
    
     

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