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Returns the natural logarithm of the complete beta function.

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Interface

#include <codecogs/maths/special/gamma/logbeta.h>

using namespace Maths::Special::Gamma;

double logBeta( 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 .size=medium

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

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

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

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Result –

logBeta

Interface

References

Parameters