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A193084 Decimal expansion of the coefficient of x in the reduction of (e^x)*cos(x) by x^2->x+1.

%I A193084 #9 Oct 23 2015 02:35:53
%S A193084 3,0,2,9,5,8,8,7,1,4,3,3,6,2,6,0,0,1,1,9,7,5,8,4,9,8,0,2,3,5,4,8,1,1,
%T A193084 3,6,5,2,9,3,9,1,8,9,2,1,9,5,4,7,5,9,8,1,0,0,5,2,4,4,4,4,7,6,5,9,5,1,
%U A193084 2,9,6,5,6,8,4,9,8,4,8,7,2,3,9,3,2,3,1,0,8,4,8,6,2,6,2,0,4,0,7,1
%N A193084 Decimal expansion of the coefficient of x in the reduction of (e^x)*cos(x) by x^2->x+1.
%C A193084 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%e A193084 -0.3029588714336260011975849802354811365293918921...
%t A193084 f[x_] := Exp[x] Cos[x]; r[n_] := Fibonacci[n];
%t A193084 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193084 u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
%t A193084 RealDigits[u0, 10]  (* A193083 *)
%t A193084 u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]
%t A193084 RealDigits[u1, 10]  (* A193084 *)
%Y A193084 Cf. A193010, A192232, A193083.
%K A193084 nonn,cons
%O A193084 0,1
%A A193084 _Clark Kimberling_, Jul 15 2011