log Beta

Returns the natural logarithm of the complete beta function.

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LogBeta
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LogBeta

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doublelogBeta(	double	`a`
	double	`b`	)

Returns the natural logarithm of the complete beta function, which is fundamentally just

$ln( \Gamma(a)*\Gamma(b) / \Gamma(a+b) )$

(1)

However when either a or b are large (typically above 8) then there are more appropriate methods of computing an accurate value efficiently. An illustration of this curve is given below:

$\graph a=0:20, b=1:5:5$

References:

DiDinato, A. R. and Morris, A. H. Algorithm 708: Significant Digit Computation of the Incomplete Beta Function Ratios. ACM Trans. Math. Softw. 18 (1993), 360-373.

Parameters

a	first symmetric argument to the complete beta function, a>0.
b	second symmetric argument to the complete beta function, b>0.

Authors

Updated by Vince Cole

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