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] > > >