Beta Function as Integral of Power of t by Power of 1 minus t over Power of r plus t
Theorem
- $\displaystyle \Beta \left({x, y}\right) := r^y \left({r + 1}\right)^x \int_{\mathop \to 0}^{\mathop \to 1} \frac {t^{x - 1} \left({1 - t}\right)^{y - 1} } {\left({r + t}\right)^{x + y} } \rd t$
where $\Beta$ denotes the Beta function.
Proof
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Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $17.6$: The Beta Function:Some Important Results
