Gold 51

Kravchuk polynomials

Gold ID

51

Link

https://sigir21.wmflabs.org/wiki/Kravchuk_polynomials#math.102.5

Formula

${\mathcal {K}}_{k}(x;n,q)=\sum _{j=0}^{k}(-q)^{j}(q-1)^{k-j}{\binom {n-j}{k-j}}{\binom {x}{j}}$

TeX Source

\mathcal{K}_k(x; n,q) = \sum_{j=0}^{k}(-q)^j (q-1)^{k-j} \binom {n-j}{k-j} \binom{x}{j}

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

\mathcal{K}_k(x; n,q) = \sum_{j=0}^{k}(-q)^j (q-1)^{k-j} \binom {n-j}{k-j} \binom{x}{j}

Expected (Gold Entry)

\KrawtchoukpolyK{k}@{x}{n}{q} = \sum_{j=0}^{k}(-q)^j (q-1)^{k-j} \binom {n-j}{k-j} \binom{x}{j}

Mathematica

Translation

Subscript[\[CapitalKappa], k][x ; n , q] == Sum[(- q)^(j)*(q - 1)^(k - j)*Binomial[n - j,k - j]*Binomial[x,j], {j, 0, k}, GenerateConditions->None]

Expected (Gold Entry)

K[k_, x_, n_, q_] := Sum[(- q)^(j)*(q - 1)^(k - j)*Binomial[n - j,k - j]*Binomial[x,j], {j, 0, k}]

Maple

Translation

Kappa[k](x ; n , q) = sum((- q)^(j)*(q - 1)^(k - j)*binomial(n - j,k - j)*binomial(x,j), j = 0..k)

Expected (Gold Entry)