Incomplete beta function

The incomplete beta function is defined by an integral,

$I_{x}(a,b)={\frac {B_{x}(a,b)}{B(a,b)}}={\frac {1}{B(a,b)}}\int _{0}^{x}t^{a-1}\,(1-t)^{b-1}\,dt$

with a > 0 and b > 0.

Properties

$I_{0}(a,b)=0\,$

$I_{1}(a,b)=1\,$

(Many other properties could be listed here.)

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. (1988) Numerical Recipes in C. Cambridge, UK: Cambridge University Press. (See section 6.3)