Krawtchouk matrices

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In mathematics, Krawtchouk matrices are matrices whose entries are values of Krawtchouk polynomials at nonnegative integer points.[1] [2] The Krawtchouk matrix K(N) is an (N+1)×(N+1) matrix. Here are the first few examples:

In general, for positive integer , the entries are given via the generating function

where the row and column indices and run from to .

These Krawtchouk polynomials are orthogonal with respect to symmetric binomial distributions, .[3]

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