Incomplete Beta Function

$\backslash mathrm\{B\}\_x(a,b)\; =\; \backslash int\_0^x\; t^\{a-1\}\backslash ,(1-t)^\{b-1\}\backslash ,\backslash mathrm\{d\}t\; \backslash !$

$I\_x(a,b)\; =\; \backslash frac\{\backslash mathrm\{B\}\_x(a,b)\}\{\backslash mathrm\{B\}(a,b)\}\; \backslash !$

Properties

$I\_0(a,b)\; =\; 0\; \backslash ,$

$I\_1(a,b)\; =\; 1\; \backslash ,$

$I\_x(a,b)\; =\; 1\; -\; I\_\{1-x\}(b,a)$

References

• M. Abramowitz and I. A. Stegun, eds. (1972) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover. (See sections 6.6 and 26.5)

• W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling. (1992) Numerical Recipes in C. Cambridge, UK: Cambridge University Press. Second edition. (See section 6.4)

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