casinh.c File Reference

#include "prim.h"
#include "math.h"
#include "complex.h"

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Functions
complex	casinh (complex z)
	Inverse hyperbolic sine of complex number. More...

Function Documentation

complex casinh

(

complex

z

)

Inverse hyperbolic sine of complex number.

Version

1.0

Date

14/09/15

Inverse hyperbolic sine expressed using complex logarithms:

asinh(z) = log(z + sqrt(z*z + 1))

With branch cuts: -i INF to -i and i to i INF

Domain: -INF to INF
Range:  -INF to INF

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

Definition at line 48 of file casinh.c.

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

Referenced by ComplexNumber::HypArcSine().

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

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