Orthogonal Polynomials - 18.3 Definitions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
18.3.E1	${\displaystyle{\displaystyle\sum_{n=1}^{N+1}T_{j}\left(x_{N+1,n}\right)T_{k}\left(x_{N+1,n}\right)=0}}$ \sum_{n=1}^{N+1}\ChebyshevpolyT{j}@{x_{N+1,n}}\ChebyshevpolyT{k}@{x_{N+1,n}} = 0	${\displaystyle{\displaystyle 0\leq j,j\leq N,0\leq k,k\leq N,j\neq k}}$	sum(ChebyshevT(j, x[N + 1 , n])*ChebyshevT(k, x[N + 1 , n]), n = 1..N + 1) = 0	Sum[ChebyshevT[j, Subscript[x, N + 1 , n]]*ChebyshevT[k, Subscript[x, N + 1 , n]], {n, 1, N + 1}, GenerateConditions->None] == 0	Skipped - Unable to analyze test case: Null	Skipped - Unable to analyze test case: Null	-	-
18.3.E2	${\displaystyle{\displaystyle x_{N+1,n}=\cos\left((n-\tfrac{1}{2})\pi/(N+1)\right)}}$ x_{N+1,n} = \cos@{(n-\tfrac{1}{2})\pi/(N+1)}		x[N + 1 , n] = cos((n -(1)/(2))*Pi/(N + 1))	Subscript[x, N + 1 , n] == Cos[(n -Divide[1,2])*Pi/(N + 1)]	Failure	Failure	Failed [298 / 300] Result: .1432026267+.3500908026*I Test Values: {N = 1/2*3^(1/2)+1/2*I, x[N+1,n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: 1.718798807+.233214116e-1*I Test Values: {N = 1/2*3^(1/2)+1/2*I, x[N+1,n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [298 / 300] Result: Complex[0.14320262643759762, 0.350090802645732] Test Values: {Rule[n, 1], Rule[N, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, Plus[1, N], n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.7187988066024098, 0.023321411689447014] Test Values: {Rule[n, 2], Rule[N, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, Plus[1, N], n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data