casech.c File Reference

#include "prim.h"

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Functions
complex	casech (complex z)
	Inverse hyperbolic secant of complex numbers. More...

Function Documentation

casech()

complex casech

(

complex

z

)

Inverse hyperbolic secant of complex numbers.

Inverse hyperbolic secant expressed using complex logarithms:

asech(z) = log(sqrt(1 / (z * z) - 1) + 1/z)

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

Definition at line 42 of file casech.c.

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

Referenced by ComplexNumber::HypArcSecant().

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

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