This function evaluates a generalization of Pochhammer's symbol.

Function Return Value

POCH — Function value.   (Output)
The generalized Pochhammer symbol is Γ(a + x)/ Γ(a).

Required Arguments

A — The first argument.   (Input)

X — The second, differential argument.   (Input)

FORTRAN 90 Interface

Generic:                              POCH (A, X)

Specific:                             The specific interface names are S_POCH and D_POCH.

FORTRAN 77 Interface

Single:                                POCH (A, X)

Double:                              The double precision function name is DPOCH.

Description

Pochhammer's symbol is (a)n = (a)(a  − 1)…(a − n + 1) for n a nonnegative integer. Pochhammer's generalized symbol is defined to be

See GAMMA for the definition of Γ(x).

Note that a straightforward evaluation of Pochhammer's generalized symbol with either gamma or log gamma functions can be especially unreliable when a is large or x is small.

Substantial loss can occur if a + x or a are close to a negative integer unless |x| is sufficiently small. To insure that the result does not overflow or underflow, one can keep the arguments a and a + x well within the range dictated by the gamma function routine GAMMA or one can keep |x| small whenever a is large. POCH also works for a variety of arguments outside these rough limits, but any more general limits that are also useful are difficult to specify.

Comments

Informational error

Type Code

3         2                  Result of POCH(A, X) is accurate to less than one-half precision because the absolute value of the X is too large. Therefore, A + X cannot be evaluated accurately.

3         2                  Result of POCH(A, X) is accurate to less than one-half precision because either A or A + X is too close to a negative integer.

For X a nonnegative integer, POCH(A, X) is just Pochhammer's symbol.

 

Example

In this example, (1.6)_0.8 is computed and printed.

 

      USE POCH_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      REAL       A, VALUE, X

 !                                 Compute

      A     = 1.6

      X     = 0.8

      VALUE = POCH(A, X)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) A, X, VALUE

99999 FORMAT (' POCH(', F6.3, ',', F6.3, ') = ', F6.4)

      END

Output

 

POCH( 1.600, 0.800) = 1.3902

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