Heun Functions - 31.3 Basic Solutions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
31.3.E1	${\displaystyle{\displaystyle\mathit{H\!\ell}\left(a,q;\alpha,\beta,\gamma,\delta;z\right)=\sum_{j=0}^{\infty}c_{j}z^{j}}}$ \HeunHl@{a}{q}{\alpha}{\beta}{\gamma}{\delta}{z} = \sum_{j=0}^{\infty}c_{j}z^{j}	${\displaystyle{\displaystyle|z|<1}}$	HeunG(a, q, alpha, beta, gamma, delta, z) = sum(c[j]*(z)^(j), j = 0..infinity)	Error	Failure	Missing Macro Error	Manual Skip!	-
31.3.E2	${\displaystyle{\displaystyle a\gamma c_{1}-qc_{0}=0}}$ a\gamma c_{1}-qc_{0} = 0		a*gamma*c[1]- q*c[0] = 0	a*\[Gamma]*Subscript[c, 1]- q*Subscript[c, 0] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
31.3.E3	${\displaystyle{\displaystyle R_{j}c_{j+1}-(Q_{j}+q)c_{j}+P_{j}c_{j-1}=0}}$ R_{j}c_{j+1}-(Q_{j}+q)c_{j}+P_{j}c_{j-1} = 0	${\displaystyle{\displaystyle j\geq 1}}$	(a*(j + 1)*(j + gamma))*c[j + 1]-(Q[j]+ q)*c[j]+ P[j]*c[j - 1] = 0	(a*(j + 1)*(j + \[Gamma]))*Subscript[c, j + 1]-(Subscript[Q, j]+ q)*Subscript[c, j]+ Subscript[P, j]*Subscript[c, j - 1] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-