BetaRegularized[z, a, b] == BetaRegularized[z, a - n, b] - ((z^(a - 1) (1 - z)^b)/(Beta[a, b] (a + b - 1))) Sum[Pochhammer[1 - a, k]/(z^k Pochhammer[2 - a - b, k]), {k, 0, n - 1}] /; Element[n, Integers] && n >= 0

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2001-10-29