catanh.c File Reference

#include "prim.h"

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Functions
complex	catanh (complex z)
	Inverse hyperbolic tangent of complex number. More...

Function Documentation

catanh()

complex catanh

(

complex

z

)

Inverse hyperbolic tangent of complex number.

Inverse hyperbolic tangent expressed using complex logarithms:

atanh(z) = 1/2 * ((log(1 + z) - log(1 - z))

More info is available at Wikipedia:
https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation

Definition at line 42 of file catanh.c.

References cadd(), clog(), cmul(), cpack(), and csub().

Referenced by ComplexNumber::HypArcTangent().

{
    complex half = cpack(0.5, 0.0);
    complex one = cpack(1.0, 0.0);
    complex a = clog(cadd(one, z));
    complex b = clog(csub(one, z));
    complex c = csub(a, b);
    complex w = cmul(half, c);
    return w;
}

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