This function evaluates the hyperbolic cosine integral.

Function Return Value

CHI — Function value.   (Output)

Required Arguments

X — Argument for which the function value is desired.   (Input)

FORTRAN 90 Interface

Generic:                              CHI (X)

Specific:                             The specific interface names are S_CHI and D_CHI.

FORTRAN 77 Interface

Single:                                CHI (X)

Double:                              The double precision function name is DCHI.

Description

The hyperbolic cosine integral, Chi(x), is defined to be

 

where γ ≈ 0.57721566 is Euler's constant.

The argument x must be large enough that e−x/x does not underflow, and x must be small enough that ex does not overflow.

Comments

When X is negative, the principal value is used.

Example

In this example, Chi(2.5) is computed and printed.

 

      USE CHI_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      REAL       VALUE, X

!                                 Compute

      X     = 2.5

      VALUE = CHI(X)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' CHI(', F6.3, ') = ', F6.3)

      END

Output

 

CHI(2.500) =  3.524

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