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 GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

## 5.6 Inverse Complex Trigonometric Functions

Function: gsl_complex gsl_complex_arcsin (gsl_complex z)
This function returns the complex arcsine of the complex number z, \arcsin(z). The branch cuts are on the real axis, less than -1 and greater than 1.
Function: gsl_complex gsl_complex_arcsin_real (double z)
This function returns the complex arcsine of the real number z, \arcsin(z). For z between -1 and 1, the function returns a real value in the range [-\pi/2,\pi/2]. For z less than -1 the result has a real part of -\pi/2 and a positive imaginary part. For z greater than 1 the result has a real part of \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, \arccos(z). The branch cuts are on the real axis, less than -1 and greater than 1.
Function: gsl_complex gsl_complex_arccos_real (double z)
This function returns the complex arccosine of the real number z, \arccos(z). For z between -1 and 1, the function returns a real value in the range [0,\pi]. For z less than -1 the result has a real part of \pi and a negative imaginary part. For z greater than 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, \arctan(z). The branch cuts are on the imaginary axis, below -i and above i.
Function: gsl_complex gsl_complex_arcsec (gsl_complex z)
This function returns the complex arcsecant of the complex number z, \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, \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, \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, \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, \arccot(z) = \arctan(1/z).
 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition