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 A201946 Decimal expansion of x>0 satisfying x*sinh(x)=2. 6
 1, 2, 4, 9, 3, 9, 4, 3, 3, 6, 6, 4, 6, 3, 2, 4, 4, 7, 2, 5, 1, 1, 2, 7, 4, 3, 2, 1, 2, 6, 1, 0, 0, 8, 1, 2, 3, 4, 6, 9, 4, 4, 1, 3, 0, 0, 9, 0, 1, 5, 2, 9, 6, 9, 6, 2, 9, 7, 2, 6, 0, 7, 6, 8, 6, 8, 8, 2, 1, 2, 3, 9, 7, 3, 1, 0, 6, 2, 2, 9, 8, 3, 0, 0, 5, 3, 2, 5, 7, 7, 0, 8, 2, 8, 6, 5, 3, 9, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For many choices of u and v, there is exactly one x>0 satisfying x*sinh(u*x)=v.  Guide to related sequences, with graphs included in Mathematica programs: u.... v.... x 1.... 1.... A133867 1.... 2.... A201946 1.... 3.... A202243 2.... 1.... A202244 3.... 1.... A202245 2.... 2.... A202284 Suppose that f(x,u,v) is a function of three real variables and that g(u,v) is a function defined implicitly by f(g(u,v),u,v)=0.  We call the graph of z=g(u,v) an implicit surface of f. For an example related to A199597, take f(x,u,v)=x*sinh(ux)-v and g(u,v) = a nonzero solution x of f(x,u,v)=0.  If there is more than one nonzero solution, care must be taken to ensure that the resulting function g(u,v) is single-valued and continuous.  A portion of an implicit surface is plotted by Program 2 in the Mathematica section. LINKS EXAMPLE x=1.2493943366463244725112743212610081234694... MATHEMATICA (* Program 1:  A201946 *) u = 1; v = 2; f[x_] := x*Sinh[u*x]; g[x_] := v Plot[{f[x], g[x]}, {x, 0, 2}, {AxesOrigin -> {0, 0}}] r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110] RealDigits[r]   (* A201946 *) (* Program 2: implicit surface of u*sinh(x)=v *) f[{x_, u_, v_}] := x*Sinh[u*x] - v; t = Table[{u, v, x /. FindRoot[f[{x, u, v}] == 0, {x, 0, .2}]}, {v, 0, 10}, {u, 1, 4}]; ListPlot3D[Flatten[t, 1]] (* for A201946 *) CROSSREFS Cf. A201939. Sequence in context: A081344 A227272 A021405 * A341352 A301514 A269063 Adjacent sequences:  A201943 A201944 A201945 * A201947 A201948 A201949 KEYWORD nonn,cons AUTHOR Clark Kimberling, Dec 15 2011 STATUS approved

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Last modified July 31 22:39 EDT 2021. Contains 346377 sequences. (Running on oeis4.)