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%I A193085 #6 Mar 30 2012 18:57:38
%S A193085 1,1,6,6,3,4,7,3,4,8,1,9,0,8,6,4,5,4,0,4,8,1,3,2,1,6,5,5,4,7,0,2,0,1,
%T A193085 7,2,3,9,5,9,3,0,1,2,3,1,1,8,9,4,4,5,7,2,1,4,3,5,9,2,0,7,2,5,7,0,8,4,
%U A193085 1,5,3,4,1,0,5,8,7,1,2,2,6,8,7,1,3,1,6,0,4,9,7,5,9,5,2,9,9,3,6,1
%N A193085 Decimal expansion of the constant term of the reduction of (e^x)*sin(x) by x^2->x+1.
%C A193085 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%e A193085 constant=1.166347348190864540481321655470201723
%e A193085 ...
%t A193085 f[x_] := Exp[x] Sin[x]; r[n_] := Fibonacci[n];
%t A193085 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193085 u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
%t A193085 RealDigits[u0, 10]  (* A193085 *)
%t A193085 u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]
%t A193085 RealDigits[u1, 10]  (* A193086 *)
%Y A193085 Cf. A193010, A192232, A193086.
%K A193085 nonn,cons
%O A193085 1,3
%A A193085 _Clark Kimberling_, Jul 15 2011

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