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A245320 Coefficients of "optimum L" polynomials L_n(ω^2) ordered by increasing powers.

%I A245320 #9 Feb 13 2023 09:00:05
%S A245320 0,0,1,0,0,1,0,1,-3,3,0,0,3,-8,6,0,1,-8,28,-40,20,0,0,6,-40,105,-120,
%T A245320 50,0,1,-15,105,-355,615,-525,175,0,0,10,-120,615,-1624,2310,-1680,
%U A245320 490,0,1,-24,276,-1624,5376,-10416,11704,-7056,1764,0,0,15,-280
%N A245320 Coefficients of "optimum L" polynomials L_n(ω^2) ordered by increasing powers.
%C A245320 Used in the generation of "optimum L" (or Legendre-Papoulis) filters.
%D A245320 A. Papoulis, ”On Monotonic Response Filters,” Proc. IRE, 47, No. 2, Feb. 1959, 332-333 (correspondence section)
%H A245320 C. Bond, <a href="http://www.crbond.com/papers/optf2.pdf">Optimum “L” Filters: Polynomials, Poles and Circuit Elements</a>, 2004.
%H A245320 C. Bond, <a href="http://www.crbond.com/papers/lopt.pdf">Notes on “L” (Optimal) Filters</a>, 2011.
%H A245320 A. Papoulis, <a href="https://doi.org/10.1109/JRPROC.1958.286876">Optimum Filters with Monotonic Response</a>, Proc. IRE, 46, No. 3, March 1958, pp. 606-609.
%e A245320 Triangle begins:
%e A245320 0;
%e A245320 0, 1;
%e A245320 0, 0,  1;
%e A245320 0, 1, -3,   3;
%e A245320 0, 0,  3,  -8,  6;
%e A245320 0, 1, -8,  28, -40,   20;
%e A245320 0, 0,  6, -40, 105, -120, 50;
%e A245320 ...
%e A245320 So:
%e A245320 L_4(ω^2) = 0 + 0ω^2 + 3ω^4 -  8ω^6 +  6ω^8
%e A245320 L_5(ω^2) = 0 + 1ω^2 - 8ω^4 + 28ω^6 - 40ω^8 + 20ω^10
%Y A245320 Derived from A100258 and A060818.
%K A245320 sign,tabl
%O A245320 0,9
%A A245320 _Jonathan Bright_, Jul 17 2014