casec.c File Reference

#include "prim.h"

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Functions
complex	casec (complex z)
	Inverse secant expressed using complex logarithms: More...

Function Documentation

casec()

complex casec

(

complex

z

)

Inverse secant expressed using complex logarithms:

Inverse secant expressed using complex logarithms:

arcsec z = -i * log(i * sqr(1 - 1/(z*z)) + 1/z)

More info is available at Wikipedia:
https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms

Definition at line 42 of file casec.c.

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

Referenced by ComplexNumber::ArcSecant().

{
    complex one = cpack(1.0, 0.0);
    complex i = cpack(0.0, 1.0);
    complex j = cpack(0.0, -1.0);
    complex rz = creci(z);
    complex z2 = cmul(z, z);
    complex p = cdiv(one, z2);
    complex q = csqrt(csub(one, p));
    complex w = cmul(j, clog(cadd(cmul(i, q), rz)));
    return w;
}

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