for $b_{0} \geq 8$ ,

$\ln B = \ln Γ (a_{0}) + \ln \frac{Γ (b_{0})}{Γ (a_{0} + b_{0})};$
for $b_{0} < 8$ ,

$\ln B = \ln Γ (a_{0}) + \ln Γ (b_{0}) - \ln Γ (a_{0} + b_{0});$

for

2 < a_{0} < 8

a_{0}

is reduced to the interval

[1, 2]

B (a, b) = \frac{a_{0} - 1}{a_{0} + b_{0} - 1} B (a_{0} - 1, b_{0})

;

for

1 \leq a_{0} \leq 2

for $b_{0} \geq 8$ ,

$\ln B = \ln Γ (a_{0}) + \ln \frac{Γ (b_{0})}{Γ (a_{0} + b_{0})};$
for $2 < b_{0} < 8$ , $b_{0}$ is reduced to the interval $[1, 2]$ ;
for $b_{0} \leq 2$ ,

$\ln B = \ln Γ (a_{0}) + \ln Γ (b_{0}) - \ln Γ (a_{0} + b_{0}) .$

s14cbc is derived from BETALN in DiDonato and Morris (1992).

4 References

DiDonato A R and Morris A H (1992) Algorithm 708: Significant digit computation of the incomplete beta function ratios ACM Trans. Math. Software 18 360–373

5 Arguments

1: $a$ – double Input: On entry: the argument $a$ of the function.

Constraint: $a > 0.0$ .
2: $b$ – double Input: On entry: the argument $b$ of the function.

Constraint: $b > 0.0$ .
3: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL: On entry, $a = ⟨ value ⟩$ .
Constraint: $a > 0.0$ .

On entry, $b = ⟨ value ⟩$ .
Constraint: $b > 0.0$ .

7 Accuracy

s14cbc should produce full relative accuracy for all input arguments.

8 Parallelism and Performance

s14cbc is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example reads values of the arguments

a

and

b

from a file, evaluates the function and prints the results.

s14cb: FL CL CPP AD

NAG CL Interfaces14cbc (beta_​log_​real)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
s14cbc (beta_log_real)