Gold 74

Dual Hahn polynomials

Gold ID

74

Link

https://sigir21.wmflabs.org/wiki/Dual_Hahn_polynomials#math.126.7

Formula

$\sum _{s=a}^{b-1}{w}_n^{(c)}(s,a,b)w_m^{(c)}(s,a,b)\rho (s)[\mathrm{\Delta }x(s-\frac{1}{2})]={\delta }_{nm}{d}_n^2$

TeX Source

\sum^{b-1}_{s=a}w_n^{(c)}(s,a,b)w_m^{(c)}(s,a,b)\rho(s)[\Delta x(s-\frac{1}{2}) ]=\delta_{nm}d_n^2

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
	-	-

Semantic LaTeX

Translation

\sum_{s=a}^{b-1} w_n^{(c)}(s , a , b) w_m^{(c)}(s , a , b) \rho(s) [\Delta x(s - \frac{1}{2})] = \delta_{nm} d_n^2

Expected (Gold Entry)

\sum_{s=a}^{b-1} \dualHahnpolyR{n}@{c}{s}{a}{b} \dualHahnpolyR{m}@{c}{s}{a}{b} \rho(s) [\Delta x(s - \frac{1}{2})] = \delta_{nm} d_n^2

Mathematica

Translation

Sum[w[(Subscript[w, n])^(c)]*(s , a , b)*w[(Subscript[w, m])^(c)]*(s , a , b)*\[Rho][s]*(\[CapitalDelta]*x*(s -Divide[1,2])), {s, a, b - 1}, GenerateConditions->None] == Subscript[\[Delta], n, m]*(Subscript[d, n])^(2)

Expected (Gold Entry)

Maple

Translation

sum(w((w[n])^(c))*(s , a , b)*w((w[m])^(c))*(s , a , b)*rho(s)*(Delta*x*(s -(1)/(2))), s = a..b - 1) = delta[n, m]*(d[n])^(2)

Expected (Gold Entry)