Orthogonal Polynomials - 18.38 Mathematical Applications

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
18.38.E1	${\displaystyle{\displaystyle V_{n}(x)=\ifrac{2nH_{n+1}\left(x\right)H_{n-1}\left(x\right)}{(H_{n}\left(x\right))^{2}}}}$ V_{n}(x) = \ifrac{2n\HermitepolyH{n+1}@{x}\HermitepolyH{n-1}@{x}}{(\HermitepolyH{n}@{x})^{2}}		V[n](x) = (2*n*HermiteH(n + 1, x)*HermiteH(n - 1, x))/((HermiteH(n, x))^(2))	Subscript[V, n][x] == Divide[2*n*HermiteH[n + 1, x]*HermiteH[n - 1, x],(HermiteH[n, x])^(2)]	Failure	Aborted	Failed [90 / 90] Result: -.256517449+.7500000000*I Test Values: {x = 3/2, V[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -.905043527+.7500000000*I Test Values: {x = 3/2, V[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [90 / 90] Result: Complex[-0.25651744987889735, 0.7499999999999999] Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[Subscript[V, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.905043526976403, 0.7499999999999999] Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[Subscript[V, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.38.E3	${\displaystyle{\displaystyle\sum_{m=0}^{n}P^{(\alpha,0)}_{m}\left(x\right)\geq 0}}$ \sum_{m=0}^{n}\JacobipolyP{\alpha}{0}{m}@{x} \geq 0	${\displaystyle{\displaystyle-1\leq x,x\leq 1,\alpha>-1}}$	sum(JacobiP(m, alpha, 0, x), m = 0..n) >= 0	Sum[JacobiP[m, \[Alpha], 0, x], {m, 0, n}, GenerateConditions->None] >= 0	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 27]