COSH

The function extends FORTRAN’s generic function COSH to evaluate the complex hyperbolic cosine.

Function Return Value

COSH — Complex function value. (Output)

Required Arguments

Z — Complex number representing the angle in radians for which the hyperbolic cosine is desired. (Input)

FORTRAN 90 Interface

Generic: COSH (Z)

Specific: The specific interface names are CCOSH and ZCOSH.

FORTRAN 77 Interface

Complex: CCOSH (Z)

Double complex:  The double complex function name is ZCOSH.

Description

Let ɛ = AMACH(4) be the machine precision. If ∣ℑz∣ is larger than

 

then the result will be less than half precision, and a recoverable error condition is reported. If ∣ℑz∣ is larger than 1/ɛ, the result has no precision and a fatal error is reported. Finally, if ∣ℜz∣ is too large, the result overflows and a fatal error results. Here, ℜz and ℑz represent the real and imaginary parts of z, respectively.

Example

In this example, cosh(‑2 + 2i) is computed and printed.

 

USE COSH_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

COMPLEX VALUE, Z

! Compute

Z = (-2.0, 2.0)

VALUE = COSH(Z)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) Z, VALUE

99999 FORMAT (' COSH((', F6.3, ',', F6.3, ')) = (',&

F6.3, ',', F6.3, ')')

END

Output

 

COSH((-2.000, 2.000)) = (-1.566,-3.298)