Numerical Methods - 3.6 Linear Difference Equations
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 3.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n}w_{n+1}-b_{n}w_{n}+c_{n}w_{n-1} = 0}
a_{n}w_{n+1}-b_{n}w_{n}+c_{n}w_{n-1} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a[n]*w[n + 1]- b[n]*w[n]+ c[n]*w[n - 1] = 0 |
Subscript[a, n]*Subscript[w, n + 1]- Subscript[b, n]*Subscript[w, n]+ Subscript[c, n]*Subscript[w, n - 1] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\lambda_{n}w_{n} = 1}
\sum_{n=0}^{\infty}\lambda_{n}w_{n} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(lambda[n]*w[n], n = 0..infinity) = 1 |
Sum[Subscript[\[Lambda], n]*Subscript[w, n], {n, 0, Infinity}, GenerateConditions->None] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.6.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{n+1}w_{n} = p_{n}w_{n+1}+e_{n}}
p_{n+1}w_{n} = p_{n}w_{n+1}+e_{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | p[n + 1]*w[n] = p[n]*w[n + 1]+ exp(1)[n] |
Subscript[p, n + 1]*Subscript[w, n] == Subscript[p, n]*Subscript[w, n + 1]+ Subscript[E, n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.6.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{n+1}-2nw_{n}+w_{n-1} = 0}
w_{n+1}-2nw_{n}+w_{n-1} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w[n + 1]- 2*n*w[n]+ w[n - 1] = 0 |
Subscript[w, n + 1]- 2*n*Subscript[w, n]+ Subscript[w, n - 1] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.6.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{n+1}-2nw_{n}+w_{n-1} = -(2/\cpi)(1-(-1)^{n})}
w_{n+1}-2nw_{n}+w_{n-1} = -(2/\cpi)(1-(-1)^{n}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w[n + 1]- 2*n*w[n]+ w[n - 1] = -(2/Pi)*(1 -(- 1)^(n))
|
Subscript[w, n + 1]- 2*n*Subscript[w, n]+ Subscript[w, n - 1] == -(2/Pi)*(1 -(- 1)^(n))
|
Failure | Failure | Failed [300 / 300] Result: 1.273239544+0.*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 1}
Result: -1.732050808-1.000000000*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 2}
Result: -2.190862072-2.000000000*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 3}
Result: -.927858596e-1+.3660254040*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = -1/2+1/2*I*3^(1/2), n = 1}
... skip entries to safe data |
Failed [300 / 300]
Result: 1.2732395447351628
Test Values: {Rule[n, 1], Rule[Subscript[w, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-1.7320508075688774, -0.9999999999999999]
Test Values: {Rule[n, 2], Rule[Subscript[w, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |
| 3.6.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n}w_{n+1}-b_{n}w_{n} = d_{n}}
a_{n}w_{n+1}-b_{n}w_{n} = d_{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a[n]*w[n + 1]- b[n]*w[n] = d[n] |
Subscript[a, n]*Subscript[w, n + 1]- Subscript[b, n]*Subscript[w, n] == Subscript[d, n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |