Orthogonal Polynomials - 18.3 Definitions
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 18.3.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=1}^{N+1}\ChebyshevpolyT{j}@{x_{N+1,n}}\ChebyshevpolyT{k}@{x_{N+1,n}} = 0}
\sum_{n=1}^{N+1}\ChebyshevpolyT{j}@{x_{N+1,n}}\ChebyshevpolyT{k}@{x_{N+1,n}} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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
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Sum[ChebyshevT[j, Subscript[x, N + 1 , n]]*ChebyshevT[k, Subscript[x, N + 1 , n]], {n, 1, N + 1}, GenerateConditions->None] == 0
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Skipped - Unable to analyze test case: Null | Skipped - Unable to analyze test case: Null | - | - |
| 18.3.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{N+1,n} = \cos@{(n-\tfrac{1}{2})\pi/(N+1)}}
x_{N+1,n} = \cos@{(n-\tfrac{1}{2})\pi/(N+1)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | x[N + 1 , n] = cos((n -(1)/(2))*Pi/(N + 1))
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Subscript[x, N + 1 , n] == Cos[(n -Divide[1,2])*Pi/(N + 1)]
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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 |