amath  1.8.5
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ccoth.c File Reference
#include "prim.h"
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Functions

complex ccoth (complex z)
 Hyperbolic cotangent of a complex number. More...
 

Function Documentation

◆ ccoth()

complex ccoth ( complex  z)

Hyperbolic cotangent of a complex number.

acoth(z) = 0.5 * (log(1 + 1/z) - log(1 - 1/z))

or

a+bi
               sinh(2.0 * a)
real  = ---------------------------—
         cosh(2.0 * a) - cos(2.0 * b)
  -sin(2.0 * b)
imag = ---------------------------— cosh(2.0 * a) - cos(2.0 * b)

Definition at line 50 of file ccoth.c.

References cimag(), cos(), cosh(), cpack(), creal(), sin(), and sinh().

Referenced by ComplexNumber::HypCotangent().

51 {
52  complex w;
53  double a, b;
54  double d;
55 
56  a = creal(z);
57  b = cimag(z);
58  d = cosh(2.0 * a) - cos(2.0 * b);
59  w = cpack(sinh(2.0 * a) / d, -sin(2.0 * b) / d);
60 
61  return w;
62 }
double sin(double x)
Sine function.
Definition: sin.c:86
double cosh(double x)
Hyperbolic cosine function.
Definition: cosh.c:83
Definition: mathi.h:48
complex cpack(double x, double y)
Pack two real numbers into a complex number.
Definition: prim.c:68
double cimag(complex z)
Imaginary part of complex number.
Definition: prim.c:46
double cos(double x)
Cosine function.
Definition: cos.c:87
double sinh(double x)
Hyperbolic sine function.
Definition: sinh.c:77
double creal(complex z)
Real part of complex number.
Definition: prim.c:38
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