What is the Beta Function?
The Beta Function is a special mathematical function widely used in probability theory, statistics, and calculus. It is defined as:
\[ B(x, y) = \int_0^1 t^{x-1} (1-t)^{y-1} \, dt \]
Alternatively, it can also be expressed using the Gamma Function:
\[ B(x, y) = \frac{\Gamma(x) \cdot \Gamma(y)}{\Gamma(x + y)} \]
This function is commonly applied in problems involving integrals, distribution calculations, and more.
Example
For \( x = 10 \) and \( y = 8 \), the Beta Function is:
\[ B(10, 8) = 5.141917 \times 10^{-6} \, \text{(Scientific Notation)} \]
\[ B(10, 8) = 0.00000514191690662279 \, \text{(Full Decimal)} \]
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