Inverse Complex Trigonometric Functions

Function: gsl_complex gsl_complex_arcsin (gsl_complex z)

This function returns the complex arcsine of the complex number z, @math{\arcsin(z)}. The branch cuts are on the real axis, less than @math{-1} and greater than @math{1}.

Function: gsl_complex gsl_complex_arcsin_real (double z)

This function returns the complex arcsine of the real number z, @math{\arcsin(z)}. For @math{z} between @math{-1} and @math{1}, the function returns a real value in the range @math{(-\pi,\pi]}. For @math{z} less than @math{-1} the result has a real part of @math{-\pi/2} and a positive imaginary part. For @math{z} greater than @math{1} the result has a real part of @math{\pi/2} and a negative imaginary part.

Function: gsl_complex gsl_complex_arccos (gsl_complex z)

This function returns the complex arccosine of the complex number z, @math{\arccos(z)}. The branch cuts are on the real axis, less than @math{-1} and greater than @math{1}.

Function: gsl_complex gsl_complex_arccos_real (double z)

This function returns the complex arccosine of the real number z, @math{\arccos(z)}. For @math{z} between @math{-1} and @math{1}, the function returns a real value in the range @math{[0,\pi]}. For @math{z} less than @math{-1} the result has a real part of @math{\pi/2} and a negative imaginary part. For @math{z} greater than @math{1} the result is purely imaginary and positive.

Function: gsl_complex gsl_complex_arctan (gsl_complex z)

This function returns the complex arctangent of the complex number z, @math{\arctan(z)}. The branch cuts are on the imaginary axis, below @math{-i} and above @math{i}.

Function: gsl_complex gsl_complex_arcsec (gsl_complex z)

This function returns the complex arcsecant of the complex number z, @math{\arcsec(z) = \arccos(1/z)}.

Function: gsl_complex gsl_complex_arcsec_real (double z)

This function returns the complex arcsecant of the real number z, @math{\arcsec(z) = \arccos(1/z)}.

Function: gsl_complex gsl_complex_arccsc (gsl_complex z)

This function returns the complex arccosecant of the complex number z, @math{\arccsc(z) = \arcsin(1/z)}.

Function: gsl_complex gsl_complex_arccsc_real (double z)

This function returns the complex arccosecant of the real number z, @math{\arccsc(z) = \arcsin(1/z)}.

Function: gsl_complex gsl_complex_arccot (gsl_complex z)

This function returns the complex arccotangent of the complex number z, @math{\arccot(z) = \arctan(1/z)}.