cacsc.c File Reference

#include "prim.h"

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Functions
complex	cacsc (complex z)
	Inverse cosecant of complex number. More...

Function Documentation

cacsc()

complex cacsc

(

complex

z

)

Inverse cosecant of complex number.

Inverse cosecant expressed using complex logarithms:

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

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

Definition at line 42 of file cacsc.c.

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

Referenced by ComplexNumber::ArcCosecant().

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

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