DLMF:18.23.E3 (Q5904)

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DLMF:18.23.E3
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    ( 1 - 1 - p p ⁢ z ) x ⁢ ( 1 + z ) N - x = ∑ n = 0 N ( N n ) ⁢ K n ⁡ ( x ; p , N ) ⁢ z n , superscript 1 1 𝑝 𝑝 𝑧 𝑥 superscript 1 𝑧 𝑁 𝑥 superscript subscript 𝑛 0 𝑁 binomial 𝑁 𝑛 Krawtchouk-polynomial-K 𝑛 𝑥 𝑝 𝑁 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\left(1-\frac{1-p}{p}z\right)^{x}(1+z)^{N-x}=\sum_% {n=0}^{N}\genfrac{(}{)}{0.0pt}{}{N}{n}K_{n}\left(x;p,N\right)z^{n},}}
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    DLMF:18.23.E3
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