This function evaluates the binomial coefficient.

Function Return Value

BINOM — Function value.   (Output)
See Comment 1.

Required Arguments

N — First parameter of the binomial coefficient.   (Input)
N must be nonnegative.

M — Second parameter of the binomial coefficient.   (Input)
M must be nonnegative and less than or equal to N.

FORTRAN 90 Interface

Generic:                              BINOM (N, M)

Specific:                             The specific interface names are S_BINOM and D_BINOM.

FORTRAN 77 Interface

Single:                                BINOM (N, M)

Double:                              The double precision function name is DBINOM.

Description

The binomial function is defined to be

 

 

with n ≥ m ≥ 0. Also, n must not be so large that the function overflows.

Comments

1.         If the generic version of this function is used, the immediate result must be stored in a variable before use in an expression. For example:

X = BINOM(9, 5) Y = SQRT(X)

            must be used rather than

Y = SQRT(BINOM(9, 5)).

            If this is too much of a restriction on the programmer, then the specific name can be used without this restriction.

2.         To evaluate binomial coefficients for nonintegral values of the arguments, the complete beta function or log beta function should be used.

Example

In this example,  is computed and printed.

 

      USE BINOM_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    M, N, NOUT

      REAL       VALUE

!                                 Compute

      N     = 9

      M     = 5

      VALUE = BINOM(N, M)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) N, M, VALUE

99999 FORMAT (' BINOM(', I1, ',', I1, ') = ', F6.2)

      END

Output

 

BINOM(9,5) = 126.00

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