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 ε = 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/ε, 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)

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