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MathGroup Archive 2006

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Correction: new procedure for converting a new recursive polynomial set into matrices

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70731] Correction: new procedure for converting a new recursive polynomial set into matrices
  • From: Roger Bagula <rlbagula at sbcglobal.net>
  • Date: Wed, 25 Oct 2006 01:39:56 -0400 (EDT)
  • References: <ehkcmn$jn9$1@smc.vnet.net>

I was getting a "shift" function type of output.
It took some work to get the numbers lined up right.
The signs in the two triangular sequences still come up different!

Clear[p, a, b]
p[0, x] = 1; p[1, x] = x - 1;
p[k_, x_] := p[k, x] = p[k - 1, x] - x^2*p[k - 2, x]
Table[Expand[p[n, x]], {n, 0, 10}]
Table[Sum[CoefficientList[p[n, x], x][[m]], {m, 1, n + 1}], {n, 0, 20}]
w = Table[CoefficientList[p[n, x], x], {n, 0, 20}]
Flatten[w]
MatrixForm[w]
An[d_] := Table[If[n == d, -w[[n]][[m]], If[m == n, 1, 0]], {n, 2, d}, {m,
     1, d - 1}]
Table[An[d], {d, 2, 19}]
Table[CharacteristicPolynomial[An[d], x], {d, 2, 19}]
b = Join[{{1}},
      Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 
2, 19}]]
Flatten[%]
MatrixForm[b]

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