Does anyone have an effective strategy to evaluate the following integral? Is it perhaps some known special function? \begin{align} & \int_0^1 p^x (1-p)^{n-x} \frac{B\left( y+sp, m-y+s-sp \right)}{B\left( sp, s-sp \right)} \,\mathrm{d}p \\ = \, & \frac{\Gamma(s)}{\Gamma(m+s)} \int_0^1 p^x (1-p)^{n-x} \frac{\Gamma\left( y + sp \right)}{\Gamma\left( sp \right)}\frac{\Gamma\left( y+s-sp \right)}{\Gamma\left( s-sp \right)} \,\mathrm{d}p \end{align} Here $x,y$ are natural numbers, $n \geq x$ is a natural number, and $s$ is any positive number.
2026-03-28 06:09:11.1774678151
Evaluating an integral involving Beta function ratio
81 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in INTEGRATION
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