(a + b)ⁿ = Σ_{k=0..n} C(n,k) a^(n-k) b^k. Generalises Pascal's triangle and grounds generating-function combinatorics.
Binomial theorem
Related concepts
- Combination C(n,k) = nCr
- Gaussian (normal) distribution
- Stirling numbers
- Sperner / LYM inequality
- Lucas' theorem (binomial coefficients)
- Semiconductor radiation detectors (HPGe, Si)
- Negative-binomial burden: VMR=1+μ/k; aggregation parameter k; overdispersion
- Hardy-Weinberg: p² + 2pq + q² = (p+q)² = 1; F2 3:1 and 9:3:3:1
- Wright-Fisher model framework
- V(D)J recombination (Tonegawa 1976)