The formula to calculate the Bernstein Coefficient (B(n, k)) is:
\[ B(n, k) = \frac{n!}{k!(n-k)!} \]
Where:
A Bernstein coefficient is a value used in Bernstein polynomials, which are a particular set of polynomials used in approximation theory. These coefficients are used to express a polynomial in terms of Bernstein basis polynomials. The Bernstein polynomial of degree \( n \) is a linear combination of Bernstein basis polynomials of the same degree, and the coefficients of this linear combination are the Bernstein coefficients. These coefficients are useful in various applications, including computer graphics, numerical analysis, and the approximation of functions.
Let's assume the following values:
Using the formula to calculate the Bernstein Coefficient:
\[ B(5, 2) = \frac{5!}{2!(5-2)!} = \frac{5!}{2!3!} = \frac{120}{2 \times 6} = \frac{120}{12} = 10 \]
The Bernstein Coefficient \( B(5, 2) \) is 10.
