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Krawtchouk Polynomials

Definition

The Krawtchouk polynomials are defined as

\[ \begin{align} K_n(x;p,N) &= {N \choose n}^{-1} \sum_{k=0}^n {N-x \choose n-k} {x \choose k} \left(1-\frac{1}{p}\right)^k\\ &= {}_2F_1 \left(\left. {-n, -x \atop -N} \; \right| \frac{1}{p} \right) \end{align} \]

Difference Equation

Recurrence Equation

Parameters

Variables

\(n\)

\(x\)

Parameters

\(p\) \(0 < p < 1\)

\(N\) \(N > 0\)

factor (use Maple-style input)

   hypergeometric term in \(n\) and hypergeometric term in \(x\) required