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A201944 Decimal expansion of x>0 satisfying x*cosh(2x)=1.

%I A201944 #8 Feb 07 2025 16:44:07
%S A201944 5,7,5,2,9,2,4,8,3,7,0,9,3,3,1,9,7,4,7,6,7,4,6,6,8,6,6,8,0,6,8,9,4,0,
%T A201944 9,7,8,8,3,4,1,8,7,4,7,4,2,2,1,2,1,1,7,0,5,9,1,6,9,6,2,5,9,0,4,4,1,6,
%U A201944 1,2,7,3,0,8,8,2,0,5,8,6,4,0,0,6,8,3,7,7,2,0,7,2,6,2,3,4,9,7,9
%N A201944 Decimal expansion of x>0 satisfying x*cosh(2x)=1.
%C A201944 See A201939 for a guide to related sequences. The Mathematica program includes a graph.
%H A201944 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201944 0.5752924837093319747674668668068940978834187...
%t A201944 u = 2; v = 1;
%t A201944 f[x_] := x*Cosh[u*x]; g[x_] := v
%t A201944 Plot[{f[x], g[x]}, {x, 0, 1}, {AxesOrigin -> {0, 0}}]
%t A201944 r = x /. FindRoot[f[x] == g[x], {x, .57, .58}, WorkingPrecision -> 110]
%t A201944 RealDigits[r]    (* A201944 *)
%Y A201944 Cf. A201939.
%K A201944 nonn,cons
%O A201944 0,1
%A A201944 _Clark Kimberling_, Dec 15 2011