Gold 67

Heine–Stieltjes polynomials

Gold ID

67

Link

https://sigir21.wmflabs.org/wiki/Heine–Stieltjes_polynomials#math.119.0

Formula

${\frac {d^{2}S}{dz^{2}}}+\left(\sum _{j=1}^{N}{\frac {\gamma _{j}}{z-a_{j}}}\right){\frac {dS}{dz}}+{\frac {V(z)}{\prod _{j=1}^{N}(z-a_{j})}}S=0$

TeX Source

\frac{d^2 S}{dz^2}+\left(\sum _{j=1}^N \frac{\gamma _j}{z - a_j} \right) \frac{dS}{dz} + \frac{V(z)}{\prod _{j=1}^N (z - a_j)}S = 0

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
	-	-

Semantic LaTeX

Translation

\deriv [2]{S}{z} +(\sum_{j=1}^N \frac{\StieltjesConstants{j}}{z - a_j}) \frac{dS}{dz} + \frac{V(z)}{\prod _{j=1}^N (z - a_j)} S = 0

Expected (Gold Entry)

\deriv [2]{S}{z} +(\sum_{j=1}^N \frac{\gamma _j}{z - a_j}) \deriv[]{S}{z} + \frac{V(z)}{\prod _{j=1}^N (z - a_j)} S = 0

Mathematica

Translation

D[S, {z, 2}]+(Sum[Divide[Subscript[\[Gamma], j],z - Subscript[a, j]], {j, 1, N}, GenerateConditions->None])*Divide[d*S,d*z]+Divide[V[z],Product[z - Subscript[a, j], {j, 1, N}, GenerateConditions->None]]*S == 0

Expected (Gold Entry)

Maple

Translation

diff(S, [z$(2)])+(sum((gamma(j))/(z - a[j]), j = 1..N))*(d*S)/(d*z)+(V(z))/(product(z - a[j], j = 1..N))*S = 0

Expected (Gold Entry)