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26.2 Incomplete Beta
The incomplete beta function, B(x;a,b), is defined for x∈[0,1] and a,b≥0 such that a+b≠0 by \text{B}(x; \, a, b) \ = \ \int_0^x u^{a - 1} \, (1 - u)^{b - 1} \, du, `< where \text{B}(a, b) is the beta function defined in appendix. If x = 1, the incomplete beta function reduces to the beta function, \text{B}(1; a, b) = \text{B}(a, b).
The regularized incomplete beta function divides the incomplete beta function by the beta function, I_x(a, b) \ = \ \frac{\text{B}(x; \, a, b)}{B(a, b)} \, .