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CATANH(3)                               BSD Library Functions Manual                               CATANH(3)

NAME
     catanh -- complex inverse hyperbolic tangent function

SYNOPSIS
     double complex
     catanh(double complex z);

     long double complex
     catanhl(long double complex z);

     float complex
     catanhf(float complex z);

DESCRIPTION
     catanh(z) computes the inverse hyperbolic tangent of the complex floating-point number z, with branch
     cuts outside the interval [-1, 1] along the real axis.

     catanh() returns values in a strip of the complex plane with imaginary part in the interval [-Pi/2,
     Pi/2].

     For all complex floating point numbers z,

           catanh(conj(z)) = conj(catanh(z)).
           catanh(-z) = -catanh(z)

SPECIAL VALUES
     The symmetries of catanh() are used to abbreviate the specification of special values.

     catanh(_ + _i) returns 0 + 0 i.

     catanh(_ + NaN i) returns 0 + NaN i.

     catanh(1 + _i) returns inf + 0i and raises the divide-by-zero flag.

     catanh(x + inf i) returns 0 + Pi/2 i, for finite positive-signed x.

     catanh(x + NaN i) returns NaN + NaN i, for non-zero finite x.

     catanh(inf + yi) returns 0 + Pi/2 i, for finite positive-signed y.

     catanh(inf + inf i) returns 0 + Pi/2 i.

     catanh(inf + NaN i) returns 0 + NaN i.

     catanh(NaN + yi) returns NaN + NaN i, for finite y.

     catanh(NaN + inf i) returns 0 + Pi/2 i.

     catanh(NaN + NaN i) returns NaN + NaN i.

NOTES
SEE ALSO
     ctanh(3) complex(3)

STANDARDS
     The catanh() function conforms to ISO/IEC 9899:1999(E).

4th Berkeley Distribution                     December 11, 2006                    4th Berkeley Distribution