Heun Functions - 31.14 General Fuchsian Equation

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
31.14.E1	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\left(\sum_{j=1}^{N}\frac{\gamma_{j}}{z-a_{j}}\right)\frac{\mathrm{d}w}{\mathrm{d}z}+\left(\sum_{j=1}^{N}\frac{q_{j}}{z-a_{j}}\right)w=0}}$ \deriv[2]{w}{z}+\left(\sum_{j=1}^{N}\frac{\gamma_{j}}{z-a_{j}}\right)\deriv{w}{z}+\left(\sum_{j=1}^{N}\frac{q_{j}}{z-a_{j}}\right)w = 0	${\displaystyle{\displaystyle\sum_{j=1}^{N}q_{j}=0}}$	diff(w, [z$(2)])+(sum((gamma[j])/(z - a[j]), j = 1..N))*diff(w, z)+(sum((q[j])/(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]+(Sum[Divide[Subscript[q, j],z - Subscript[a, j]], {j, 1, N}, GenerateConditions->None])*w == 0	Skipped - Unable to analyze test case: Null	Skipped - Unable to analyze test case: Null	-	-
31.14#Ex1	${\displaystyle{\displaystyle\alpha+\beta+1=\sum_{j=1}^{N}\gamma_{j}}}$ \alpha+\beta+1 = \sum_{j=1}^{N}\gamma_{j}		alpha + beta + 1 = sum(gamma[j], j = 1..N)	\[Alpha]+ \[Beta]+ 1 == Sum[Subscript[\[Gamma], j], {j, 1, N}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
31.14#Ex2	${\displaystyle{\displaystyle\alpha\beta=\sum_{j=1}^{N}a_{j}q_{j}}}$ \alpha\beta = \sum_{j=1}^{N}a_{j}q_{j}		alpha*beta = sum(a[j]*q[j], j = 1..N)	\[Alpha]*\[Beta] == Sum[Subscript[a, j]*Subscript[q, j], {j, 1, N}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
31.14.E3	${\displaystyle{\displaystyle w(z)=\left(\prod_{j=1}^{N}(z-a_{j})^{-\gamma_{j}/2}\right)W(z)}}$ w(z) = \left(\prod_{j=1}^{N}(z-a_{j})^{-\gamma_{j}/2}\right)W(z)		w(z) = (product((z - a[j])^(- gamma[j]/2), j = 1..N))*W(z)	w[z] == (Product[(z - Subscript[a, j])^(- Subscript[\[Gamma], j]/2), {j, 1, N}, GenerateConditions->None])*W[z]	Skipped - no semantic math	Skipped - no semantic math	-	-