Heun Functions - 31.15 Stieltjes Polynomials

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
31.15.E1	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\left(\sum_{j=1}^{N}\frac{\gamma_{j}}{z-a_{j}}\right)\frac{\mathrm{d}w}{\mathrm{d}z}+\frac{\Phi(z)}{\prod_{j=1}^{N}(z-a_{j})}w=0}}$ \deriv[2]{w}{z}+\left(\sum_{j=1}^{N}\frac{\gamma_{j}}{z-a_{j}}\right)\deriv{w}{z}+\frac{\Phi(z)}{\prod_{j=1}^{N}(z-a_{j})}w = 0		diff(w, [z$(2)])+(sum((gamma[j])/(z - a[j]), j = 1..N))*diff(w, z)+(Phi(z))/(product(z - a[j], j = 1..N))*w = 0	D[w, {z, 2}]+(Sum[Divide[Subscript[\[Gamma], j],z - Subscript[a, j]], {j, 1, N}, GenerateConditions->None])*D[w, z]+Divide[\[CapitalPhi][z],Product[z - Subscript[a, j], {j, 1, N}, GenerateConditions->None]]*w == 0	Failure	Failure	Error	Failed [300 / 300] Result: Times[Complex[0.0, 1.0], Power[NProduct[0 Test Values: {j, 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]}, Rule[GenerateConditions, None]], -1]], {Rule[N, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Φ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[γ, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Times[Complex[0.0, 1.0], Power[NProduct[0 Test Values: {j, 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]}, Rule[GenerateConditions, None]], -1]], {Rule[N, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Φ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[γ, j], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
31.15#Ex1	${\displaystyle{\displaystyle\gamma_{j}>0}}$ \gamma_{j} > 0		gamma[j] > 0	Subscript[\[Gamma], j] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
31.15.E7	${\displaystyle{\displaystyle q_{j}=\gamma_{j}\sum_{k=1}^{n}\frac{1}{z_{k}-a_{j}}}}$ q_{j} = \gamma_{j}\sum_{k=1}^{n}\frac{1}{z_{k}-a_{j}}	${\displaystyle{\displaystyle j=1}}$	q[j] = gamma[j]*sum((1)/(z[k]- a[j]), k = 1..n)	Subscript[q, j] == Subscript[\[Gamma], j]*Sum[Divide[1,Subscript[z, k]- Subscript[a, j]], {k, 1, n}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-