This function evaluates the complete beta function.
Function Return Value
BETA — Function value. (Output)
Required Arguments
A — First beta
parameter. (Input)
For real arguments, A must be
positive.
B — Second beta
parameter. (Input)
For real arguments, B must be
positive.
FORTRAN 90 Interface
Generic: BETA (A, B)
Specific: The specific interface names are S_BETA, D_BETA, and C_BETA.
FORTRAN 77 Interface
Single: BETA (A, B)
Double: The double precision function name is DBETA.
Complex: The complex name is CBETA.
Description
The beta function is defined to be
See GAMMA for the definition of Γ(x).
For real arguments the function BETA requires that both arguments be positive. In addition, the arguments must not be so large that the result underflows.
For complex arguments, the arguments a and a + b must not be close to negative integers. The arguments should not be so large (near the real axis) that the result underflows. Also, a + b should not be so far from the real axis that the result overflows.
Comments
Informational error
Type Code
2 1 The function underflows because A and/or B is too large.
Example 1
In this example, β(2.2, 3.7) is computed and printed.
USE BETA_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
REAL A, VALUE, X
! Compute
A = 2.2
X = 3.7
VALUE = BETA(A, X)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) A, X, VALUE
99999 FORMAT (' BETA(', F6.3, ',', F6.3, ') = ', F6.4)
END
Output
BETA( 2.200, 3.700) = 0.0454
Additional Example
Example 2
In this example, β(1.7 + 2.2i, 3.7 + 0.4i) is computed and printed.
USE BETA_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
COMPLEX A, B, VALUE
! Compute
A = (1.7, 2.2)
B = (3.7, 0.4)
VALUE = BETA(A, B)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) A, B, VALUE
99999 FORMAT (' BETA((', F6.3, ',', F6.3, '), (', F6.3, ',', F6.3,&
')) = (', F6.3, ',', F6.3, ')')
END
Output
BETA(( 1.700, 2.200), ( 3.700, 0.400)) = (-0.033,-0.017)
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